Permutations/Combinations (1 Viewer)

[currysauce]

Argh i hate this stuff

Can someone explain how to do this question

In how many ways can the letters of the word permute be arranged if the vowels and consonants occupy alternate places?

 

[mojako]

in the word permute:
you have 4 consonants and 3 vowels (two of which are identical)
they need to be in alternate places --(1)

you can re-word condition (1) as
"consonants are grouped together and vowels are grouped together" --(2)

if you try to visualise it, condition (1) and condition (2) give the same number of possible arangements.

so, no of ways: 4! * 3! / 2! * 2
4! is to select consonants
3! is to select vowels
2! is for the two identical vowels
2 is to choose whether we start the word with a vowel or a consonant

I think I'm right but someone needs to confirm this.

 

[Constip8edSkunk]

u dont need to multiply it by 2 as only consonants can start

 

[mojako]

u dont need to multiply it by 2 as only consonants can start

didnt you mean: only vowels can start?

 

[Constip8edSkunk]

i meant theres 4 consonant and 3 vowels so it can only be of the format:

CVCVCVC

where C represent a consonant and V a vowel

 

[mojako]

oh yes, I forgot about that.