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

A 210

B 1050

C 25200

D 21400

Correct Answer: Option C

Number of ways of selecting (3 consonants out of 7) and (2 vowels out of 4)

= (7C3x 4C2)

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

= 210.

Number of groups, each having 3 consonants and 2 vowels = 210.

Each group contains 5 letters.

Number of ways of arranging

5 letters among themselves = 5!

= 5 x 4 x 3 x 2 x 1

= 120.

So, Required number of ways

= (210 x 120) = 25200.