Find the number of ways of selecting 9 balls | vedclass

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(C) To select $9$ balls such that there are $3$ balls of each colour,we need to choose $3$ red balls from $6$,$3$ white balls from $5$,and $3$ blue ba

Vedclass · Accepted Answer

$2000$

Vedclass · Answer

(C) To select $9$ balls such that there are $3$ balls of each colour,we need to choose $3$ red balls from $6$,$3$ white balls from $5$,and $3$ blue balls from $5$.The number of ways to choose $3$ red balls from $6$ is given by $C(6,3) = \frac{6!}{3!3!} = \frac{6 	imes 5 	imes 4}{3 	imes 2 	imes 1} = 20$.The number of ways to choose $3$ white balls from $5$ is given by $C(5,3) = \frac{5!}{3!2!} = \frac{5 	imes 4}{2 	imes 1} = 10$.The number of ways to choose $3$ blue balls from $5$ is given by $C(5,3) = \frac{5!}{3!2!} = \frac{5 	imes 4}{2 	imes 1} = 10$.By the fundamental principle of counting,the total number of ways is the product of these individual selections:$p = 20 	imes 10 	imes 10 = 2000$.

Find the number of ways of selecting $9$ balls from $6$ red balls,$5$ white balls,and $5$ blue balls,if each selection consists of $3$ balls of each colour.

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