Question

Out of 5 consonants, 4 vowels and 3 capitals how many words can be formed each containing 3 consonants, 2 vowels and beginning with a capital?

Answer 1

Cap.(3) Con.(5) Vow(4)
${}^3{C}_1{.}^5{C}_3{.}^4{C}_2\times 5!$
$=3\times 10\times 6\times 120=216000$.
Note: $5!$ and not $6!$ as capital letter is fixed in the beginning.