Hi, I need help with the question;

Determine the number of ways of arranging the letters in the wordif:handle

a) the first letter must and consonant

b) the second and fifth letter must be a vowel

Thanks

Printable View

- Nov 28th 2008, 08:44 AMCarrickCombinatorics: permutations help
Hi, I need help with the question;

Determine the number of ways of arranging the letters in the wordif:*handle*

a) the first letter must and consonant

b) the second and fifth letter must be a vowel

Thanks - Nov 28th 2008, 09:01 AMInti
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; thatīs a permutation of 5 elements: $\displaystyle 5!$

Doing the same with the other consonants it means that you have $\displaystyle 4.5!=480$ 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 $\displaystyle 2.4!=48$

Iīm assuming there are no repeated letters on an arrangement. - Nov 28th 2008, 09:10 AMCarrick
Thanks for help, you explained it well.