# 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 5Cways.

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 $=\left({ }^{4} C_{2} \times{ }^{5} C_{3}\right) \times 5 !=60 \times 120=7200$

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