Question

Let Y={a,b,c,d,e,f,i,j} and a 4letter word is to be formed without replacement.How many words can be formed if the word must contain both vowels and consonants?

Answer 1

There are `10800` possibilities

Explanation:

The number of words can be calculated as:

`n=3*5*6*5*4! =10800`

How was this expression created?

First I chose 1 vowel from 3 (a,e,i), next I chose 1 consonant from 5:
{b,c,d,f,j}, next I chose 2 letters from remaining 6 (the set Y contained 8 letters, I already used 2).

Final multiplication by `4!` is to calculate all possible permutations of 4 chosen letters.