# Permutations and Combinations

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• Jan 10th 2013, 09:54 AM
Twinkie
Permutations and Combinations
I'm having some issues with the word problems. Can you show me how to do them.

Deturmine the number of difforent arrangements using the letters of the word ACCESSES that:
A. Begin with exactly two S's.
B Begin with at least two S's.
• Jan 10th 2013, 10:11 AM
Plato
Re: Permutations and Combinations
Quote:

Originally Posted by Twinkie
Deturmine the number of difforent arrangements using the letters of the word ACCESSES that:
A. Begin with exactly two S's.
B Begin with at least two S's.

First, do you understand the total number of ways to arrange $\displaystyle ACCESSES$ is $\displaystyle \frac{8!}{(2!)^2\cdot(3!)}$ and why?

If not, you must start there

Then the answer to part a) is just the number of ways to arrange $\displaystyle ACCEES$ minus the number of ways to arrange $\displaystyle ACCEE$.

You tell us why that is true.
• Jan 10th 2013, 10:30 AM
Twinkie
Re: Permutations and Combinations
Yes, I understand that ACCESSES is 8!/ 2x2x3! ,because there is 8 letters and two C's, 3 S's, and 2 E's.
So for A, I count all the S's as one in the top half of the equaision like 6!/2x2 ( Now I know what I was doing wrong befor, I was counting the S's as 2 not 1). Then I subtract the equasion without any S's ,So 5!/2x2 ,with the first answer to get the final answer. To get 150, I finally got it right. Thankyou so much! :)