The number of ways in which the following pri | vedclass

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(A) There are $4$ first prizes (Mathematics,Physics,Chemistry,English) and $2$ second prizes (Mathematics,Physics).Since a boy can win more than one f

Vedclass · Accepted Answer

$20^4 	imes 19^2$

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(A) There are $4$ first prizes (Mathematics,Physics,Chemistry,English) and $2$ second prizes (Mathematics,Physics).Since a boy can win more than one first prize,each of the $4$ first prizes can be awarded in $20$ ways. Thus,the total ways to award the first prizes is $20 	imes 20 	imes 20 	imes 20 = 20^4$.For the second prizes,a boy who has already won a first prize in a subject cannot win the second prize in that same subject. Therefore,for the second prize in Mathematics,there are $19$ remaining boys available. Similarly,for the second prize in Physics,there are $19$ remaining boys available.Thus,the total number of ways to award the prizes is $20^4 	imes 19^2$.

The number of ways in which the following prizes can be given to a class of $20$ boys,first and second Mathematics,first and second Physics,first Chemistry,and first English is:

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