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I have an assignment on Permutations and Combinations and was wondering if some of you could go over my work and ensure that I have this aced. I really need to get my math mark up for University admissions so I need to ace this assignment.

Thanks a lot for your help!

-Jonathan

1) In how many distinguishable ways can the letters of the word MISSISSIPPI be arranged?

Number of distinguishable arrangements = 11!/(4!4!2!) = 34,650

2) Find the number of ways of arranging all the letters AAABBBCCDD in a row so that no two A's are side-by-side.

Number of arrangements = 7!/(3!3!2!2!) = 35

what I did: I paired the letter A up with another letter, by viewing them as 1 letter no 2 A's would ever be side by side. This makes 7 letters, and then I divided out the repeats.

3) How many distinguishable four letter arrangements can be made from teh letters of the word MISSISSIPPI?

Number of four letter arrangements = (ways with no repeats) + (ways with all 4 letters repeated) + (ways with 2 doubles) + (ways with a triple and a single)

= (4c4)x4 + (2c1) + (3c2)x(4!/2!2!) + (2c1)(1c1)x(4!/3!)

= 24 + 2 + 18 + 8

= 52

*****If it is unclear what I have done hear please ask me*****

Those are the first 3 questions out of 5. I want to make sure I'm on the right track before I finish the next 2, as they are significantly more difficult.

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# Permutations/Combinations - Could someone please check my work?

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