Question

Consider the word AARDVARKS.

a) Determine all the permutations of all the letters

b) Determine all the permutations of the letters in which the three A's are together.

Okay so for part a the answer is 30240. I'm not really sure how I should get this answer. There are a total of 9 letters in the word, but only 6 unique ones. I was thinking it would be something like 6 * 6 * 6 * 5 * 4 * 3 * 2 * 1, but that's way off. Could someone give me a nudge in the right direction?

Answer 1

a. all permutations = 8!/3!2! = 3360 <-------

b. 6 positions for AAA (123 through 678),
5!/2! permutations for the rest, so 6*5!/2! = 360 <-------

Answer 2

Sorry for my late reply, but the answer for is 30240 and the answer for b is 2520. I'm not really following what you're saying.

Answer 3

Never mind I got it for A it's 9! / 3! * 2! and for B it's 7! / 2!