Out of 12 consonants and 5 vowels, how many words, each containing 3

Question:

Out of 12 consonants and 5 vowels, how many words, each containing 3 consonants and 2 vowels, can be formed?

Solution:

3 consonants out of 12 consonants can be chosen in ${ }^{12} C_{3}$ ways. 2 vowels out

of 5 vowels can be chosen in ${ }^{5} \mathrm{C}_{2}$ ways. And also 5 letters can be written in 5 ! Ways. Therefore, the number of words can be formed is $\left({ }^{12} C_{3} X^{5} C_{2} X 5 !\right)=264000$.

 

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