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Permutation and Combination

Q1: 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

ANS:C - 25200

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.



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