Out of seven consonants and 4 vowels, how many words of 3 consonants and 2 vowel

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Question
Out of seven consonants and 4 vowels, how many words of 3 consonants and 2 vowels can be formed ?
Options
A. 25200
B. 25000
C. 25225
D. 24752

Correct Answer

25200

Explanation

Number of ways of selecting (3 consonants out of 7) and (2 vowels out of 4) =( $C_{3}^{7} � C_{2}^{4}$ ) = 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! = 120.

Required number of words = (210 x 120) = 25200.

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