Find the number of ways of selecting 9 balls | vedclass

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Question

(A) We need to select $9$ balls such that $3$ balls are of each colour (red,white,and blue).Number of ways to select $3$ red balls from $6$ is $^{6}C_

Vedclass · Accepted Answer

$2000$

Vedclass · Answer

(A) We need to select $9$ balls such that $3$ balls are of each colour (red,white,and blue).Number of ways to select $3$ red balls from $6$ is $^{6}C_{3} = \frac{6 	imes 5 	imes 4}{3 	imes 2 	imes 1} = 20$.Number of ways to select $3$ white balls from $5$ is $^{5}C_{3} = \frac{5 	imes 4 	imes 3}{3 	imes 2 	imes 1} = 10$.Number of ways to select $3$ blue balls from $5$ is $^{5}C_{3} = \frac{5 	imes 4 	imes 3}{3 	imes 2 	imes 1} = 10$.By the multiplication principle,the total number of ways is $20 	imes 10 	imes 10 = 2000$.

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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