# How Many Words of 3 Consonants and 2 Vowels can be Formed?

Out of 7 consonants and 4 vowels, how many words of 3 consonants and 2 vowels can be formed?

- 2400
- 25200
- 24100
- 20030

**Answer: (2) 25200**

**Explanation:-
**The number of groups, each having 3 consonants and 2 vowels =

^{7}C

_{3}x

^{4}C

_{2}

= (7 x 6 x 5/3 x 2 x 1) x (4 x 3 /2 x 1)

= 35 x 6

= 210

Each group contains 5 letters

Then, the number of groups of 5 letters = 5! {n! = (n-1) (n – 2) (n – 3) (n – 4) ……… }

= 5 x 4 x 3 x 2 x 1

= 120

The number of ways = 210 x 120

= 25200.

Hence, the answer is (2) 25200