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Question

# Four fair dice D1,D2,D3 and D4 each having six faces numbered 1, 2, 3, 4, 5 and 6 are rolled simultaneously. The probability that D4 shows a number appearing on one of D1,D2 and D3, is ?

A

91216

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B

108216

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C

125216

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D

127216

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Solution

## The correct option is A 91216 Sample space 6×6×6×6=64 favourable events = Case I or Case II or Case III Case I First we should select one number for D4 which apperars on all i.e. 6C1×1. Case II For D4 there are 6C1 ways. Now, it appears on any one of D1,D2 and D3 i.e. 3C1×1. For other two there are 5×5 ways. ⇒6C1×3C1×1×5×5 Case III For D4 there are 6C1 ways now it appears on any two of D1,D2 and D3 ⇒3C2×12 For other one there are 5 ways. ⇒6C1×3C2×12×5 Thus, probability =6C1+6C1×3C1×52+6C1×3C2×564 6(1+75+15)64=91216

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