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Q: permutation and combination ( Answered,   2 Comments )
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

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 =

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."

Search terms used:
 permutation word letters order

That's it!

Google Answers Researcher
Subject: Re: permutation and combination
From: xarqi-ga on 28 Mar 2005 17:24 PST
Subject: Re: permutation and combination
From: b7rk-ga on 24 Jul 2005 14:32 PDT
choose 3 elements by 3C2 and then arrange them by 2!


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