# Thread: Combinatorics: permutations help

1. ## Combinatorics: permutations help

Hi, I need help with the question;
Determine the number of ways of arranging the letters in the word handle if:
a) the first letter must and consonant
b) the second and fifth letter must be a vowel

Thanks

2. a)First letter a consonant, did I read well?
Suppose you put the H in the first place; you get
H _ _ _ _ _ that means you have 5 letters to put in 5 places; that´s a permutation of 5 elements: $5!$
Doing the same with the other consonants it means that you have $4.5!=480$ ways.

b) _ vowel _ _ vowel _

and you only have two possibilities:
_ A _ _ E _ (permutation of 4 elements)
or
_ E _ _ A _ (permutation of 4 elements)

that leads to $2.4!=48$

I´m assuming there are no repeated letters on an arrangement.

3. Thanks for help, you explained it well.