Question

In how many different ways can I arrange the following lists?

a) ABCDEFGHIJ
b) ABCDEFGHII
c) AAAAABBBBB

Answer 1

a) I can rearrange that into 10! different lists, including the original arrangement.
b) one element, I, is repeated twice, I find the ways that I can rearrange II, which is 2!. Now I can rearrange ABCDEFGHII in 10!/2! ways

Answer 2

which is 1814400

Answer 3

c), A and B are both repeated five times each. I can rearrange AAAAA 5! times, and BBBBB 5! times.

Therefore, I can rearrange AAAAABBBBB 10!/(5! * 5!) times, which is 252

Answer 4

Check my answers

Answer 5

I am sorry, I don't have time to help now. :(
I couldn't remember the approach exactly, and used all my time to catch up on how to do and left no time to do it!

Answer 6

I can check later if no one else does it for you

Answer 7

by the way; C is correct

Answer 8

lets check for that last one.

AABB, how many ways can I arrange that (easier) list?

AABB
ABAB
ABBA
BAAB
BABA
BBAA

which is 4!/(2! * 2!) = 3 * 2 = 6 ways

Answer 9

I feel enlightened

Answer 10

a) 10!
b) 10!/2!
c) 10!/(5!5!)
I agree with all your answers (but you didn't need me to tell you that!).