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Question

Total number of words formed by 2 vowels and 3 consonants taken from 4 vowels and 5 consonants is equal to
(a) 60
(b) 120
(c) 7200
(d) none of these

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Solution

(c) 7200
2 out of 4 vowels can be chosen in 4C2 ways and 3 out of 5 consonants can be chosen in 5C3 ways.
Thus, there are C2× 5C43 groups, each containing 2 vowels and 3 consonants.
Each group contains 5 letters that can be arranged in 5! ways.
∴ Required number of words = 4C2× 5C3× 5! = 60 × 120 = 7200

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