# Q.5.     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.

S seema garhwal

There are 6 red balls, 5 white balls and 5 blue balls.

9 balls have to be selected in such a way that consists of 3 balls of each colour.

3 balls are selected from 6 red balls in $^6C_3$.

3 balls are selected from 5 white balls in $^5C_3$

3 balls are selected from 5 blue balls in $^5C_3$.

Hence, by the multiplication principle, the number of ways of selecting 9 balls $=^6C_3\times ^5C_3\times ^5C_3$

$=\frac{6!}{3!3!}\times \frac{5!}{2!3!}\times \frac{5!}{2!3!}$

$=20\times 10\times 10=2000$

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