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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
Options
60
120
7200
none of these
Solution
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 \[\left( C_2 \times {}^5 {C^4}_3 \right)\] groups, each containing 2 vowels and 3 consonants.
Each group contains 5 letters that can be arranged in 5! ways.
∴ Required number of words =\[\left( {}^4 C_2 \times {}^5 C_3 \right) \times 5! = 60 \times 120 = 7200\]
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