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.


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