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?

  1. 2400
  2.  25200
  3.  24100
  4.  20030
Anurag Mishra Professor Asked on 24th September 2015 in Maths.
Add Comment
1 Answer(s)

Answer: (2) 25200

Explanation:-
The number of groups, each having 3 consonants and 2 vowels = 7C3 x 4C2
= (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

Anurag Mishra Professor Answered on 24th September 2015.
Add Comment

Your Answer

By posting your answer, you agree to the privacy policy and terms of service.