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

Answer 1

(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 $\left(C_2\times {}^5{C^4}_3\right)$ groups, each containing 2 vowels and 3 consonants.
Each group contains 5 letters that can be arranged in 5! ways.
∴ Required number of words = $\left({}^4{C}_2\times {}^5{C}_3\right)\times 5!=60\times 120=7200$