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### Discussion :: Permutation and Combination

1. Out of 7 consonants and 4 vowels, how many words of 3 consonants and 2 vowels can be formed?

2.  A. 210 B. 1050 C. 25200 D. 21400 E. None of these

Explanation :

Number of ways of selecting (3 consonants out of 7) and (2 vowels out of 4)= (7C3 x 4C2)

= [$$\frac { 7*6*5 } {3*2*1 }$$$$\frac { 4*3 } { 2*1 }$$]

= 210

Number of groups, each having 3 consonants and 2 voweL     = 210.

 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) = 2520

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