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 ?
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.
Case III For D4 there are 6C1 ways now it appears on any two of D1,D2 and D3
For other one there are 5 ways.
Thus, probability =6C1+6C1×3C1×52+6C1×3C2×564