Question

A word has 8 consonants and 3 vowels. How many distinct words can be formed if 4 consonants and 12 vowels are chosen?

Answer 1

There are 3 consonants and 3 vowels.
So, 4 consonants and 2 vowels can be selected in ⁸C₄ × ³C₂ ways.
Now, ⁸C₄ × ³C₂ 

= `((8 xx 7 xx 6 xx 5))/((4 xx 3 xx 2)) xx ((3 xx 2 xx 1))/((2 xx 1)`

= 70 × 3
= 210
Thus, there are 210 groups consisting of 4 consonants and 2 vowels.
We need to form different words from these 210 groups.
Now, each group has 6 letters.
These 6 letters can be arranged amongst themselves m 6! Ways.
∴ The number of required words
= (210) × 6!
= (210) × 720
= 151200