How many words are formed by 2 vowels and 3 consonants, taken from 4 vowels and 5 consonants?

Question:

How many words are formed by 2 vowels and 3 consonants, taken from 4 vowels and 5 consonants?

Solution:

3 consonants out of 5 consonants can be chosen in ${ }^{5} C_{3}$ ways. 2 vowels out of 

4 vowels can be chosen in ${ }^{4} \mathrm{C}_{2}$ ways. And also 5 letters can be written in $5 !$ Ways. Therefore, the number of words can be formed is $\left({ }^{5} \mathrm{C}_{3} \mathrm{X}^{4} \mathrm{C}_{2} \times 5 !\right)=7200$.

 

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