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

Question: 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

Answer: Option C

Explanation:

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

	= (7C3 x 4C2)
	= 7 x 6 x 5 x 4 x 3 3 x 2 x 1 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.

Required number of ways = (210 x 120) = 25200.

Video Explanation: https://youtu.be/dm-8T8Si5lg