Out of 7 consonants and 4 vowels, 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 ?
A. 210
B. 1050
C. 25200
D. 21400
E. None of these
Answer : C. 25200
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) / (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.
Required number of ways = (210 x 120) = 25200.
