Question

In how many ways can the following prizes be given away to a class of $20$ students, first and second in Mathematics, first and second in physics, first in Chemistry and first in English ?

Answer 1

First prize in mathematics can be given in $=30$ ways

second prize in mathematics $=29$ ways

First in physics $=30$ ways

second in physics $=29$ ways

First prize in chemistry can be given in $=30$ ways

similarly first in English $=30$ ways

All the $6$ prizes can be given in

$=30\times 29\times 30\times 29\times 30\times 30$ ways

$=681,210,000$

Total number of ways to distribute all $6$ prizes

$=681210000$