Question

How many ways are there to rearrange the letters in the word aptitude, if the first and last letter must each be a vowel?

Answer 1

I know I have to calculate how many letters to choose from. then multiply them by each other for each spot right?

Answer 2

5*26^6**5

Answer 3

right?

Answer 4

lets make it easier and say the first two letters have to be vowels (clearly makes no difference)
then4 choices for the first
3 for the second

then you have 6 letters left
the number of ways to arrange 6 letters if they are all different is \(6!=6\times 5\times 4\times 3\times 2\) but since you cannot tell the two "t" s apart, it is \(\frac{6!}{2}=6\times 5\times 4\times 3\)

Answer 5

yuuup I was wrong

Answer 6

multiply all this mess together to get your answer

Answer 7

doing so now

Answer 8

450? but I don't think that's right. working in my head not good.

Answer 9

360.

Answer 10

you have yet to multiply all the numbers satellite73 gave to you

Answer 11

yup im lost

Answer 12

4*3*6*5*4*3

Answer 13

4320