The number of ways in which 2 black and 3 red balls can be selected from a bag containing 5 black and 6 red balls is

Question

The number of ways in which 2 black and 3 red balls can be selected from a bag containing 5 black and 6 red balls is (A) 170 (B) 190 (C) 180 (D) 200

Tardigrade Admin · Accepted Answer

Out of 5 black balls, 2 black balls can be selected in

^{5} C_{2}

ways.
Out of 6 red balls, 3 red balls can be selected in

^{6} C_{3}

ways.

Hence, by FPC, total number of ways

=^{5} C_{2} \times^{6} C_{3} [∵^{n} C_{2} = \frac{n ( n - 1 )}{2}

and

^{n} C_{3} = \frac{n ( n - 1 ) ( n - 2 )}{6}]

= \frac{5 \times 4}{2} \times \frac{6 \times 5 \times 4}{6}

= 10 \times 20

= 200 ways

Q. The number of ways in which 2 black and 3 red balls can be selected from a bag containing 5 black and 6 red balls is