First slide

Combinations

Question

There are two urns. Urn A has 3 distinct red balls and urn B has 9 distinct blue balls. From each urn, two balls are taken out at random and then transferred to the other. The number of ways in which this can be done is

Easy

A

108
B

3
C

36
D

66

Solution

Number of ways to choose,
2 red balls from urn A, out of 3 distinct red balls = ${}^{3}{C_{2}}$
2 blue balls from urn B, out of 9 distinct blue balls = ${}^{9}{C_{2}}$
Total number of ways $=^{3} C_{2} \times^{9} C_{2}$
$= 3 \times \frac{9 \times 8}{2} = 3 \times 36 = 108$

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