Question

In how many ways can the following prizes be given away to a class of $20$ boys: first and second Classical, first and second Mathematical, first Science, and first French?

Answer 1

First Classical can be given to any one of the $20$ boys which is ${}^{20}{C}_1=20$
Second Classical can be given to any of the remaining $19$ boys learning the First Classical i.e. ${}^{19}{C}_1=19$.
First Maths can be given to any one of the $20$ boys which is ${}^{20}{C}_1=20$
Second Maths can be given to any of the remaining $19$ boys i.e. ${}^{19}{C}_1=19$.
First Science can be given to any of the $20$ boys.
First French can be given to any of the $20$ boys.
$\therefore$ Total Number of ways $=20\times 19\times 20\times 19\times 20\times 20$
$=57760000$