Question

Out of $25$ consonants and $5$ vowels how many words can be formed each consisting of $2$ consonants and $3$ vowels?

Answer 1

$2$ positions for the consonants can be chosen in ${}^5{C}_2=10$ ways

Hence, considering no repetition the $5$ places of the required words can be filled up in $10\times 25\times 24\times 5\times 4\times 3=360000$ ways.