- #1
rocketboy
- 243
- 1
Hey everyone,
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.
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.