When we throw a dice 4 times, the probability that the minimum number appearing on the dice is 2 and

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When we throw a dice 4 times, the probability that the minimum number appearing on the dice is 2 and the maximum is 5 is

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Sol. [Key Concept: Die rolled 4 times: probability of the stated min/max event.]$$P = \frac{4^{4} - \left( \ ^{2}C_{1}3^{4} - 2^{4} \right)}{6^{4}} = \frac{55}{648}$$Favorable number of ways$=$ Number appearing can be 2,3,4,5 only - atleast one of 2 or 5 excluded.

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