Question

In how many ways can the letters of the word 'permute' be arranged if:
a) the first and last places are occupied by consonants?
b) the vowels and consonants occupy alternate places?

Answer 1

CVCVCVC--- this is the way letters should be arranged

VCVCVCV--- there are only 3 vowels; so this order does not maintain vowel-constant in alternatre position.

3 vowels can be arranged in 3!/2! way (there are 2 E) = 3
4 constant in 4! way = 24

Answer 2

so how do you work out part a?

Answer 3

The first place needs a consonant. So 4 possibilities.
The last place needs a consonant. So 3 possibilities.
For the middle, 5! possibilities.
I get 120 x 12 = 2400.

Answer 4

the answer is 720 ways

Answer 5

The first place needs a consonant. So 4 possibilities.
The last place needs a consonant. So 3 possibilities.
For the middle, 5! possibilities. (since 2 e's , divide 2!)

you get (4*3) * 5!/2!

Answer 6

Forgot the duplicates. You are right.