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.
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  • 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.
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