Total number of words formed by 2 vowels and 3 consonants taken from 4 vowels and 5 consonants is equal to
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
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 $\left(C_{2} \times{ }^{5} C^{4}{ }_{3}\right)$ groups, each containing 2 vowels and 3 consonants.
Each group contains 5 letters that can be arranged in $5 !$ ways.
$\therefore$ Required number of words $=\left({ }^{4} C_{2} \times{ }^{5} C_{3}\right) \times 5 !=60 \times 120=7200$