Q

A bag contains 5 black and 6 red balls. Determine the number of ways in which 2 black and 3 red balls can be selected.

Q.8.     A bag contains 5 black and 6 red balls. Determine the number of ways in which 2 black and 3 red balls can be selected.

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A bag contains 5 black and 6 red balls.

2 black balls can be selected in $^5C_2$  ways and 3 red balls can be selected in $^6C_3$ ways.

Thus, using multiplication priciple, number of ways of selecting 2 black and 3 red balls  $=^5C_2 .^6C_3$

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

$=10\times 20=200$

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