Out of 10 consonants and 4 vowels, words with 6 consonants and 3 vowels are formed. The number of such words is

Out of 10 consonants and 4 vowels, words with 6 consonants and 3 vowels are formed. The number of such words is

A
$\frac{7}{11} (12!)$
B
$\frac{9}{10} (12!)$
C
$\frac{7}{10} (11!)$
D
$\frac{4}{5} (12!)$

Solution:

The number of ways of choosing 6 consonants out of 10 is $^{10} C_{6}$ and 3 vowels out of 4 in $^{4} C_{3}$ .

Thus number of such words is $(^{10} C_{4}) (^{4} C_{3}) (^{9} P_{9}) = \frac{7}{11} (12!)$

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