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 Subject: permutation and combination Category: Science > Math Asked by: slamone-ga List Price: \$10.00 Posted: 28 Mar 2005 17:15 PST Expires: 27 Apr 2005 18:15 PDT Question ID: 501682
 in how many ways can we arrange the letters of the word "boy"taking two letters at a time Subject: Re: permutation and combination Answered By: richard-ga on 28 Mar 2005 18:30 PST
 Hello and thank you for your question. Here's the 'brute force' answer: six bo ob by yb oy yo Technically, this is an example of a "Permutation of less than all," that is, number of permutations of 3 different things taken 2 at a time. This is usually symbolized as 3P2, or 3!/(2-1)! or (3*2*1)/1 = 6 Here is how Dr. Math explains it (Dr. Math uses CAT as the test word) "For our CAT example, we have: 3! 3 x 2 x 1 3_P_2 = ---- = ----------- = 6 1! 1 We can use any one of the three letters in CAT as the first member of a permutation. There are three choices for the first letter: C, A, or T. After we've chosen one of these, only two choices remain for the second letter. To find the number of permutations we multiply: 3 x 2 = 6. Note: What's a factorial? A factorial is written using an exclamation point - for example, 10 factorial is written 10! - and means multiply 10 times 9 times 8 times 7... all the way down to 1." http://www.mathforum.com/dr.math/faq/faq.comb.perm.html Search terms used: permutation word letters order That's it! Google Answers Researcher Richard.ga  