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#1 2011-12-02 01:48:41

juantheron
Member
Registered: 2011-10-19
Posts: 312

probability

Let A = {0,1,2 ..... 9}

how many  different 4-digit number that is divisible by 3

if number is choosen from set A

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#2 2011-12-02 02:29:07

careless25
Real Member
Registered: 2008-07-24
Posts: 560

Re: probability

Are we allowed to choose a number more than once? for eg can we make a 4 digit number: 9999?

And to get you started:

How do you check if a number is divisible by 3?
How many such combinations are there from your set?

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#3 2011-12-02 02:36:03

John E. Franklin
Member
Registered: 2005-08-29
Posts: 3,588

Re: probability

Assume that 0000 = 0 and 0003 = 3 and 0099 = 99 and 0999 = 999.
If this is allowable the answer is:

9999/3 or 3333 I believe.


igloo myrtilles fourmis

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#4 2011-12-02 07:03:41

bobbym
bumpkin
From: Bumpkinland
Registered: 2009-04-12
Posts: 109,606

Re: probability

Hi;

If we assume with replacement, then there are 9000 numbers(1000 - 9999 ). So there are 3000 numbers that are divisible by 3.

If we assume without replacement, then there are 9*9*8*7=4536  possible 4 digit numbers.
Of those there are 1548 that are divisble by 3.


In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

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#5 2011-12-02 07:46:28

careless25
Real Member
Registered: 2008-07-24
Posts: 560

Re: probability

If we assume without replacement, then there are 9*9*8*7=4536  possible 4 digit numbers.

I am wondering how you got 9*9 when you say without replacement.
enlighten me! big_smile

Edit: Nevermind, I see what assumption you made.

Last edited by careless25 (2011-12-02 07:49:53)

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#6 2011-12-04 02:40:48

juantheron
Member
Registered: 2011-10-19
Posts: 312

Re: probability

here we take no. without replacement

thanks to all

bobbym i want more explanation for without replacement

thanks

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#7 2011-12-04 05:05:15

bobbym
bumpkin
From: Bumpkinland
Registered: 2009-04-12
Posts: 109,606

Re: probability

To have a 4 digit number you can not have a zero up front so there are 9 choices for the first. There are 9 remaining for the second. Eight choices remaining for the third. And seven left for the fourth.

9 * 9 * 8 * 7 = 4536


In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

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#8 2011-12-05 05:02:25

reconsideryouranswer
Member
Registered: 2011-05-11
Posts: 171

Re: probability

juantheron wrote:

Let A = {0,1,2 ..... 9}

how many  different 4-digit number that is divisible by 3

if number is choosen from set A

lookagain edit wrote:

Let A = {0,1,2 ..... 9}

How many  different 4-digit numbers are divisible by 3
if each digit is chosen without replacement

from set A, and 0 cannot be a leading digit?

For each of the following, there are potentially 4! permutations,
except that 0 cannot be a leading digit, so 3! permutations
must be subtracted.  So multiply each of these representative
numbers by 18 to get the total number of permutations for
this partial group:


1023
1026
1029
1035
1038
1047
1053
1056
1062
1065
1068
1074
1083
1086
1089
---------

18(15) = 270


___________________



For this second (last) partial group,
the number of permutations for
each representative number is 4!
Then multiply by 24 to get the total
number of permutations for this
partial group:


1236
1239
1245
1248
1257
1269
1278

1347
1356
1359
1368
1389

1458
1467
1479

1569
1578

1689


2346
2349
2358
2367
2379

2457
2469
2478

2568

2679


3456
3459
3468

3567
3579

3678

3789


4569
4578


5679

6789
--------

24(39) = 936



Grand total
-------------
270 + 936 = 1,206


Signature line:

I wish a had a more interesting signature line.

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#9 2011-12-05 06:52:57

bobbym
bumpkin
From: Bumpkinland
Registered: 2009-04-12
Posts: 109,606

Re: probability

Hi;

reconsideryouranswer wrote:

]Grand total
-------------
270 + 936 = 1,206

The answer of 1206 is a little low.

Here they are:

{1023, 1026, 1029, 1032, 1035, 1038, 1047, 1053, 1056, 1059, 1062, \
1065, 1068, 1074, 1083, 1086, 1089, 1092, 1095, 1098, 1203, 1206, \
1209, 1230, 1236, 1239, 1245, 1248, 1254, 1257, 1260, 1263, 1269, \
1275, 1278, 1284, 1287, 1290, 1293, 1296, 1302, 1305, 1308, 1320, \
1326, 1329, 1347, 1350, 1356, 1359, 1362, 1365, 1368, 1374, 1380, \
1386, 1389, 1392, 1395, 1398, 1407, 1425, 1428, 1437, 1452, 1458, \
1467, 1470, 1473, 1476, 1479, 1482, 1485, 1497, 1503, 1506, 1509, \
1524, 1527, 1530, 1536, 1539, 1542, 1548, 1560, 1563, 1569, 1572, \
1578, 1584, 1587, 1590, 1593, 1596, 1602, 1605, 1608, 1620, 1623, \
1629, 1632, 1635, 1638, 1647, 1650, 1653, 1659, 1674, 1680, 1683, \
1689, 1692, 1695, 1698, 1704, 1725, 1728, 1734, 1740, 1743, 1746, \
1749, 1752, 1758, 1764, 1782, 1785, 1794, 1803, 1806, 1809, 1824, \
1827, 1830, 1836, 1839, 1842, 1845, 1854, 1857, 1860, 1863, 1869, \
1872, 1875, 1890, 1893, 1896, 1902, 1905, 1908, 1920, 1923, 1926, \
1932, 1935, 1938, 1947, 1950, 1953, 1956, 1962, 1965, 1968, 1974, \
1980, 1983, 1986, 2013, 2016, 2019, 2031, 2034, 2037, 2043, 2046, \
2049, 2058, 2061, 2064, 2067, 2073, 2076, 2079, 2085, 2091, 2094, \
2097, 2103, 2106, 2109, 2130, 2136, 2139, 2145, 2148, 2154, 2157, \
2160, 2163, 2169, 2175, 2178, 2184, 2187, 2190, 2193, 2196, 2301, \
2304, 2307, 2310, 2316, 2319, 2340, 2346, 2349, 2358, 2361, 2364, \
2367, 2370, 2376, 2379, 2385, 2391, 2394, 2397, 2403, 2406, 2409, \
2415, 2418, 2430, 2436, 2439, 2451, 2457, 2460, 2463, 2469, 2475, \
2478, 2481, 2487, 2490, 2493, 2496, 2508, 2514, 2517, 2538, 2541, \
2547, 2568, 2571, 2574, 2580, 2583, 2586, 2589, 2598, 2601, 2604, \
2607, 2610, 2613, 2619, 2631, 2634, 2637, 2640, 2643, 2649, 2658, \
2670, 2673, 2679, 2685, 2691, 2694, 2697, 2703, 2706, 2709, 2715, \
2718, 2730, 2736, 2739, 2745, 2748, 2751, 2754, 2760, 2763, 2769, \
2781, 2784, 2790, 2793, 2796, 2805, 2814, 2817, 2835, 2841, 2847, \
2850, 2853, 2856, 2859, 2865, 2871, 2874, 2895, 2901, 2904, 2907, \
2910, 2913, 2916, 2931, 2934, 2937, 2940, 2943, 2946, 2958, 2961, \
2964, 2967, 2970, 2973, 2976, 2985, 3012, 3015, 3018, 3021, 3024, \
3027, 3042, 3045, 3048, 3051, 3054, 3057, 3069, 3072, 3075, 3078, \
3081, 3084, 3087, 3096, 3102, 3105, 3108, 3120, 3126, 3129, 3147, \
3150, 3156, 3159, 3162, 3165, 3168, 3174, 3180, 3186, 3189, 3192, \
3195, 3198, 3201, 3204, 3207, 3210, 3216, 3219, 3240, 3246, 3249, \
3258, 3261, 3264, 3267, 3270, 3276, 3279, 3285, 3291, 3294, 3297, \
3402, 3405, 3408, 3417, 3420, 3426, 3429, 3450, 3456, 3459, 3462, \
3465, 3468, 3471, 3480, 3486, 3489, 3492, 3495, 3498, 3501, 3504, \
3507, 3510, 3516, 3519, 3528, 3540, 3546, 3549, 3561, 3564, 3567, \
3570, 3576, 3579, 3582, 3591, 3594, 3597, 3609, 3612, 3615, 3618, \
3621, 3624, 3627, 3642, 3645, 3648, 3651, 3654, 3657, 3672, 3675, \
3678, 3681, 3684, 3687, 3690, 3702, 3705, 3708, 3714, 3720, 3726, \
3729, 3741, 3750, 3756, 3759, 3762, 3765, 3768, 3780, 3786, 3789, \
3792, 3795, 3798, 3801, 3804, 3807, 3810, 3816, 3819, 3825, 3840, \
3846, 3849, 3852, 3861, 3864, 3867, 3870, 3876, 3879, 3891, 3894, \
3897, 3906, 3912, 3915, 3918, 3921, 3924, 3927, 3942, 3945, 3948, \
3951, 3954, 3957, 3960, 3972, 3975, 3978, 3981, 3984, 3987, 4017, \
4023, 4026, 4029, 4032, 4035, 4038, 4053, 4056, 4059, 4062, 4065, \
4068, 4071, 4083, 4086, 4089, 4092, 4095, 4098, 4107, 4125, 4128, \
4137, 4152, 4158, 4167, 4170, 4173, 4176, 4179, 4182, 4185, 4197, \
4203, 4206, 4209, 4215, 4218, 4230, 4236, 4239, 4251, 4257, 4260, \
4263, 4269, 4275, 4278, 4281, 4287, 4290, 4293, 4296, 4302, 4305, \
4308, 4317, 4320, 4326, 4329, 4350, 4356, 4359, 4362, 4365, 4368, \
4371, 4380, 4386, 4389, 4392, 4395, 4398, 4503, 4506, 4509, 4512, \
4518, 4521, 4527, 4530, 4536, 4539, 4560, 4563, 4569, 4572, 4578, \
4581, 4587, 4590, 4593, 4596, 4602, 4605, 4608, 4617, 4620, 4623, \
4629, 4632, 4635, 4638, 4650, 4653, 4659, 4671, 4680, 4683, 4689, \
4692, 4695, 4698, 4701, 4710, 4713, 4716, 4719, 4725, 4728, 4731, \
4752, 4758, 4761, 4782, 4785, 4791, 4803, 4806, 4809, 4812, 4815, \
4821, 4827, 4830, 4836, 4839, 4851, 4857, 4860, 4863, 4869, 4872, \
4875, 4890, 4893, 4896, 4902, 4905, 4908, 4917, 4920, 4923, 4926, \
4932, 4935, 4938, 4950, 4953, 4956, 4962, 4965, 4968, 4971, 4980, \
4983, 4986, 5013, 5016, 5019, 5028, 5031, 5034, 5037, 5043, 5046, \
5049, 5061, 5064, 5067, 5073, 5076, 5079, 5082, 5091, 5094, 5097, \
5103, 5106, 5109, 5124, 5127, 5130, 5136, 5139, 5142, 5148, 5160, \
5163, 5169, 5172, 5178, 5184, 5187, 5190, 5193, 5196, 5208, 5214, \
5217, 5238, 5241, 5247, 5268, 5271, 5274, 5280, 5283, 5286, 5289, \
5298, 5301, 5304, 5307, 5310, 5316, 5319, 5328, 5340, 5346, 5349, \
5361, 5364, 5367, 5370, 5376, 5379, 5382, 5391, 5394, 5397, 5403, \
5406, 5409, 5412, 5418, 5421, 5427, 5430, 5436, 5439, 5460, 5463, \
5469, 5472, 5478, 5481, 5487, 5490, 5493, 5496, 5601, 5604, 5607, \
5610, 5613, 5619, 5628, 5631, 5634, 5637, 5640, 5643, 5649, 5670, \
5673, 5679, 5682, 5691, 5694, 5697, 5703, 5706, 5709, 5712, 5718, \
5721, 5724, 5730, 5736, 5739, 5742, 5748, 5760, 5763, 5769, 5781, \
5784, 5790, 5793, 5796, 5802, 5814, 5817, 5820, 5823, 5826, 5829, \
5832, 5841, 5847, 5862, 5871, 5874, 5892, 5901, 5904, 5907, 5910, \
5913, 5916, 5928, 5931, 5934, 5937, 5940, 5943, 5946, 5961, 5964, \
5967, 5970, 5973, 5976, 5982, 6012, 6015, 6018, 6021, 6024, 6027, \
6039, 6042, 6045, 6048, 6051, 6054, 6057, 6072, 6075, 6078, 6081, \
6084, 6087, 6093, 6102, 6105, 6108, 6120, 6123, 6129, 6132, 6135, \
6138, 6147, 6150, 6153, 6159, 6174, 6180, 6183, 6189, 6192, 6195, \
6198, 6201, 6204, 6207, 6210, 6213, 6219, 6231, 6234, 6237, 6240, \
6243, 6249, 6258, 6270, 6273, 6279, 6285, 6291, 6294, 6297, 6309, \
6312, 6315, 6318, 6321, 6324, 6327, 6342, 6345, 6348, 6351, 6354, \
6357, 6372, 6375, 6378, 6381, 6384, 6387, 6390, 6402, 6405, 6408, \
6417, 6420, 6423, 6429, 6432, 6435, 6438, 6450, 6453, 6459, 6471, \
6480, 6483, 6489, 6492, 6495, 6498, 6501, 6504, 6507, 6510, 6513, \
6519, 6528, 6531, 6534, 6537, 6540, 6543, 6549, 6570, 6573, 6579, \
6582, 6591, 6594, 6597, 6702, 6705, 6708, 6714, 6720, 6723, 6729, \
6732, 6735, 6738, 6741, 6750, 6753, 6759, 6780, 6783, 6789, 6792, \
6795, 6798, 6801, 6804, 6807, 6810, 6813, 6819, 6825, 6831, 6834, \
6837, 6840, 6843, 6849, 6852, 6870, 6873, 6879, 6891, 6894, 6897, \
6903, 6912, 6915, 6918, 6921, 6924, 6927, 6930, 6942, 6945, 6948, \
6951, 6954, 6957, 6972, 6975, 6978, 6981, 6984, 6987, 7014, 7023, \
7026, 7029, 7032, 7035, 7038, 7041, 7053, 7056, 7059, 7062, 7065, \
7068, 7083, 7086, 7089, 7092, 7095, 7098, 7104, 7125, 7128, 7134, \
7140, 7143, 7146, 7149, 7152, 7158, 7164, 7182, 7185, 7194, 7203, \
7206, 7209, 7215, 7218, 7230, 7236, 7239, 7245, 7248, 7251, 7254, \
7260, 7263, 7269, 7281, 7284, 7290, 7293, 7296, 7302, 7305, 7308, \
7314, 7320, 7326, 7329, 7341, 7350, 7356, 7359, 7362, 7365, 7368, \
7380, 7386, 7389, 7392, 7395, 7398, 7401, 7410, 7413, 7416, 7419, \
7425, 7428, 7431, 7452, 7458, 7461, 7482, 7485, 7491, 7503, 7506, \
7509, 7512, 7518, 7521, 7524, 7530, 7536, 7539, 7542, 7548, 7560, \
7563, 7569, 7581, 7584, 7590, 7593, 7596, 7602, 7605, 7608, 7614, \
7620, 7623, 7629, 7632, 7635, 7638, 7641, 7650, 7653, 7659, 7680, \
7683, 7689, 7692, 7695, 7698, 7803, 7806, 7809, 7812, 7815, 7821, \
7824, 7830, 7836, 7839, 7842, 7845, 7851, 7854, 7860, 7863, 7869, \
7890, 7893, 7896, 7902, 7905, 7908, 7914, 7920, 7923, 7926, 7932, \
7935, 7938, 7941, 7950, 7953, 7956, 7962, 7965, 7968, 7980, 7983, \
7986, 8013, 8016, 8019, 8025, 8031, 8034, 8037, 8043, 8046, 8049, \
8052, 8061, 8064, 8067, 8073, 8076, 8079, 8091, 8094, 8097, 8103, \
8106, 8109, 8124, 8127, 8130, 8136, 8139, 8142, 8145, 8154, 8157, \
8160, 8163, 8169, 8172, 8175, 8190, 8193, 8196, 8205, 8214, 8217, \
8235, 8241, 8247, 8250, 8253, 8256, 8259, 8265, 8271, 8274, 8295, \
8301, 8304, 8307, 8310, 8316, 8319, 8325, 8340, 8346, 8349, 8352, \
8361, 8364, 8367, 8370, 8376, 8379, 8391, 8394, 8397, 8403, 8406, \
8409, 8412, 8415, 8421, 8427, 8430, 8436, 8439, 8451, 8457, 8460, \
8463, 8469, 8472, 8475, 8490, 8493, 8496, 8502, 8514, 8517, 8520, \
8523, 8526, 8529, 8532, 8541, 8547, 8562, 8571, 8574, 8592, 8601, \
8604, 8607, 8610, 8613, 8619, 8625, 8631, 8634, 8637, 8640, 8643, \
8649, 8652, 8670, 8673, 8679, 8691, 8694, 8697, 8703, 8706, 8709, \
8712, 8715, 8721, 8724, 8730, 8736, 8739, 8742, 8745, 8751, 8754, \
8760, 8763, 8769, 8790, 8793, 8796, 8901, 8904, 8907, 8910, 8913, \
8916, 8925, 8931, 8934, 8937, 8940, 8943, 8946, 8952, 8961, 8964, \
8967, 8970, 8973, 8976, 9012, 9015, 9018, 9021, 9024, 9027, 9036, \
9042, 9045, 9048, 9051, 9054, 9057, 9063, 9072, 9075, 9078, 9081, \
9084, 9087, 9102, 9105, 9108, 9120, 9123, 9126, 9132, 9135, 9138, \
9147, 9150, 9153, 9156, 9162, 9165, 9168, 9174, 9180, 9183, 9186, \
9201, 9204, 9207, 9210, 9213, 9216, 9231, 9234, 9237, 9240, 9243, \
9246, 9258, 9261, 9264, 9267, 9270, 9273, 9276, 9285, 9306, 9312, \
9315, 9318, 9321, 9324, 9327, 9342, 9345, 9348, 9351, 9354, 9357, \
9360, 9372, 9375, 9378, 9381, 9384, 9387, 9402, 9405, 9408, 9417, \
9420, 9423, 9426, 9432, 9435, 9438, 9450, 9453, 9456, 9462, 9465, \
9468, 9471, 9480, 9483, 9486, 9501, 9504, 9507, 9510, 9513, 9516, \
9528, 9531, 9534, 9537, 9540, 9543, 9546, 9561, 9564, 9567, 9570, \
9573, 9576, 9582, 9603, 9612, 9615, 9618, 9621, 9624, 9627, 9630, \
9642, 9645, 9648, 9651, 9654, 9657, 9672, 9675, 9678, 9681, 9684, \
9687, 9702, 9705, 9708, 9714, 9720, 9723, 9726, 9732, 9735, 9738, \
9741, 9750, 9753, 9756, 9762, 9765, 9768, 9780, 9783, 9786, 9801, \
9804, 9807, 9810, 9813, 9816, 9825, 9831, 9834, 9837, 9840, 9843, \
9846, 9852, 9861, 9864, 9867, 9870, 9873, 9876}

There are 1548 by actual count.


In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

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