Question

Determine the probability in throwing 6 fair dices, there will be exactly 4 different numbers.

Answer 1

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Answer:

This case means that there will be 2 same numbers on 2 dices and rest 4 will have different numbers

Choosing any two from the sic dices and having a common number

=> 6C2*6/6*1/6 ( Choosing any number probability = 6/6 and having the same number in other dice = 1/6)

Rest 4 dices will have 4 distinct numbers with probability = 5/6*4/6*3/6*2/6

Hence the total probability is

= 6C2*6/6*5/6*4/6*3/6*2/6*1/6 = 0.23148