Question

# A bag contains 3 yellow balls and 4 pink balls. In how many ways can 2 pink balls and 1 yellow ball can be drawn from the bag?(a) 24 ways(b) 8 ways(c) 12 ways(d) 18 ways

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Hint: For solving this problem we will directly apply one formula of selection of r objects from n objects. Then we will apply the formula in the right manner to get the correct answer.

The number of ways of selecting $r$ items from the group of $n$ distinct items is:
${}^{n}{{C}_{r}}=\dfrac{n!}{r!\left( n-r \right)!}$
Number of ways of selecting 2 pink balls from 4 pink balls $={}^{4}{{C}_{2}}=\dfrac{4!}{2!\times \left( 4-2 \right)!}=\dfrac{24}{2\times 2!}=6$ .
Number of ways of selecting 1 yellow ball from 3 yellow balls $={}^{3}{{C}_{1}}=\dfrac{3!}{1!\times \left( 3-1 \right)!}=\dfrac{6}{1\times 2!}=3$ .
The number of ways to draw 2 pink balls and 1 yellow ball $=6\times 3=18$ ways.