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

The correct option is C

7200

2 out of 4 vowels can be chosen in ${}^4{C}_2$ ways and 3 out of 5 consonants can be chosen in ${}^5{C}_3$ ways.

Thus, there are $\left(C_2{\times }^5{C}_3\right)$ groups, each containing 2 vowels and 3 consonants.

Each group contains 5 letters that can be arranged in 5! ways.

$\therefore$ Required number of words

${(}^4{C}_2{\times }^5{C}_3)\times 5!=60\times 120=7200$