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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
Permutations and Combinations
Solution:
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\left[\because { }^n C_2=\frac{n(n-1)}{2}\right. $ and $ \left.{ }^n C_3=\frac{n(n-1)(n-2)}{6}\right] $
$ =\frac{5 \times 4}{2} \times \frac{6 \times 5 \times 4}{6} $
$ =10 \times 20 $
$ =200 \text { ways }$
