How many different words, each containing 2 vowels and 3 consonants can be formed with 5 vowels and 17 consonants?

Explanation

2 out of 5 vowels and 3 out of 17 consonants can be chosen in ` 5_(C_2) times 17_(C_3)` ways.

Thus, there are ` 5_(C_2) times 17_(C_3)` groups, each containing 2 vowels and 3 consonants.

Each group contains 5 letters, which can be arranged in
`5 !` ways.

`therefore` Required number of words `=>( 5_(C_2) times 17_(C_3)) 5 !`

`=>6800 times 120=>816000`