Out of 7 consonants and 4 vowels, how many words of 3 consonants and 2 vowels can be formed?
Options:
(A) 25200
(B) 2543
(C) 2344
(D) 233445
(E) 52757 Stream of consciousness:
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.
Thus, the answer is (A).