Question

You are given 7 different consonants and 3 different vowels. You have to form three letter words each containing 2 consonants and 1 vowel so that the vowel is always in between the two consonants. How many such words can be formed?

Answer 1

Con. Vow
${}^7{C}_2{\times }^3{C}_1=21\times 3=63$ selection of 3 letter words consisting of 2 consonants and one vowel. Now vowel is to be between the consonants. Hence the arrangement will be only of the consonants i.e. $2!$
Hence $63\times 2!=126$.