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#1 2007-04-13 03:20:05

sovixi
Guest

domino problem and number of possible words

Can you check if my solutions are right?

1. 6. How many different words can you make by rearranging the letters of the
   word "LONDON"?  The words do not need to make any sense: for example
   "NOODLN" would be one word.

We can make 6! numbers of words. 6! = 6 x 5 x 4 x 3 x 2 x 1 = 720 combinations


2.A domino is a rectangular tile, containing a number between zero and six
   on each half.  Three dominoes are illustrated below.

     -----    -----     -----
     |6|5|   |0|3|  |4|4|
     -----    -----     -----

  How many distinct dominoes are there?  Note that the order of the numbers
  doesn't matter: the first domino above is the same as the domino

     -----
     |5|6|
     -----

To calculate this I used combination without repetitions.
n – 7 {0, 1, 2, 3, 4, 5, 6, 7}
k – 2 (2 fields in each domino)
n!/(k! * (n! – k!)) = 7!/(2! * 5!) = 21 distinct dominos



thanks

#2 2007-04-13 04:11:48

JaneFairfax
Member
Registered: 2007-02-23
Posts: 6,868

Re: domino problem and number of possible words

1) The 6! ways of rearrangement treat the two Os and the two Ns as distinct. Since they’re not, you have to divide by 2 (for the Os), and again by 2 (for the Ns). So the total number of permutations is 6!∕(2×2).

2) There are 7 dominoes in which the two numbers are the same (00, 11, 22, etc). Of the other dominoes, we can choose one of 7 numbers for the first domino number and one of the other 6 numbers for the other domino number, and we get 7×6. Since the order doesn’t matter, however, we divide that by 2, getting 21. So the total number of dominoes is 21 + 7 = 28.

Last edited by JaneFairfax (2007-04-13 04:14:24)

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#3 2007-04-13 04:13:42

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

Re: domino problem and number of possible words

You're nearly right for 1, but you're counting some words twice because LONDON has repeated letters. You need to divide your answer by 2 because of the two O's, and then by 2 again for the two N's, which would make your final answer 180.

For 2, your method finds the number of distinct dominoes that have different numbers. It misses out the 'doubles' though, so you need to add them on. There are 7 doubles, which means that your answer should be 28.

Edit: Gah, late by two minutes. roll


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

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#4 2007-04-13 05:54:51

sovixi
Guest

Re: domino problem and number of possible words

hey thanks a lot for your help esspecialy with "LONDON" - i didn't think about repeating letters. With domino I was considering using combination with repetitions before.

Thanks again

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