Question

In how many ways can the following prizes be given to a class of 20 boys. First and second Mathematics, first and second Physics, first Chemistry, and first English?

Answer 1

Four first prizes can be given in ${20}^4$ ways since first prize of Mathematics can be given in 20 ways, the first prize of Physics also in 20 ways, similarly first prizes of Chemistry and English can be given in 20 ways each. {Note that a boy can stand first in all the four subjects). Then two-second prizes can be given in ${19}^2$ ways since a boy cannot get both the first and second prizes:
Hence the required number of ways
= ${20}^4$ x ${19}^2$ = 57760000.