JEE Main · 2010 · 11 Apr 2010 · Offline · Permutations and Combinations

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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

(A)36
(B)66
(C)108✓ Correct
(D)3

Answer: (C)

Solution

Two balls are chosen from urn A in

(2 3) = 3

ways, and independently two from urn B in

(2 9) = 36

ways. Since the two selections are made together, the number of ways to carry out the whole transfer is the product

3 \times 36 = 108

JEE Main · 2010 · 11 Apr 2010 · Offline · Single correct option

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