Question

If 12 identical balls are to be placed in 3 identical boxes, then the probability that one of the boxes contains exactly 3 balls is

(A) 55(2/3)¹⁰

(B) 220(1/3)¹²

(C) 22(1/3)¹¹

(D) 55/3(2/3)¹¹

Answer 1

Answer is  (D) 55/3(2/3)¹¹

Choose 3 balls out of 12 in ¹²C₃ ways and distribute the remaining 9 balls in two boxes in 2⁹ ways. However, 

total number of possible ways = (3)¹²

Therefore,