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#1 2007-05-27 22:18:09

Janani
Guest

Someone Help Me

Hey, I really need help in this question! Someone help me!

Arange the alphabets in the word LETTERS
a) Find how many different possibilities are there?
b) Find out how many different possibilities are there with the alphabets R and S together.
c) Find out how many different possibilities are there with the alphabets R band S not together.

Please Help ME!!!

#2 2007-05-27 22:52:59

Devantè
Real Member
Registered: 2006-07-14
Posts: 6,400

Re: Someone Help Me

a) Standard permutations. There are 7 letters in the word 'letters' (:D), and two of the letters are repeated; E and T. There are 7 letters, so 7!/(2! 2!) = (7x6x5x4x3x2x1)/(2x1)(2x1) = 5040/4 = 1260. Understand?
b) 180x2 = 360
c) 1260-360 = 900

I kind of rushed this so I could be wrong.

Last edited by Devantè (2007-05-27 22:57:49)

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#3 2007-05-27 22:54:47

mathsyperson
Moderator
Registered: 2005-06-22
Posts: 4,900

Re: Someone Help Me

a)
"LETTERS" has 7 letters. To work out the number of arrangements there are, consider the choices you can make.

For the first letter of the arrangement, you can pick any of the 7 letters. For the 2nd letter, you can pick any except the one that you already chose for the first, giving you 6 choices for that.
Then you have 5 choices for the 3rd letter and so on.

Therefore, the total amount of combinations is 7x6x5x4x3x2x1 = 5040.
However, because LETTERS has some repeated letters, we've counted some combinations twice.
We've treated the two E's as if they were different, so we need to divide the total by 2 to get rid of the symmetry there, and we also need to do the same for the two T's.

So the final answer is 5040 ÷ 4 = 1260.

b)
Now we have another restriction, because the R and S need to be next to each other. This means that we essentially only have 6 letters to pick from, which means that the answer should be (6x5x4x3x2x1) ÷ 4 = 180. However, the R and S can either be RS or SR, so that's another choice of 2 which means that the actual answer is 180 x 2 = 360.

c)
Either the R and S are together or they aren't. Combining the two gives you all possible combinations. We know the total amount, and the amount where they are together, so they can both be used to find the amount where they are apart.

1260 - 360 = 900.


Why did the vector cross the road?
It wanted to be normal.

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#4 2007-05-27 22:57:59

Janani
Guest

Re: Someone Help Me

Thank you so much for the answers! It has been a great help! Tomorrow is my test and I was just revising! Thanks alot!

#5 2007-05-27 22:59:33

Devantè
Real Member
Registered: 2006-07-14
Posts: 6,400

Re: Someone Help Me

Hi Janani,

I've just edited my post so you can understand it a little better.

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