Latest TCS Aptitude Question SOLUTION: If six fair dice are rolled , what is the probability that each of the six numbers will appears exactly once ?

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If six fair dice are rolled , what is the probability that each of the six numbers will appears exactly once ?

Asked In TCS deepak gupta (11 years ago)

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sainath  (11 years ago)

chances of different digit appear on each dice=6!
[suppose consider a case different digits appeared on all 6 dice, then remaining chances comes by arranging these 6 numbers in all possible ways without repeating.
that is 6!]
all possible chances of a number appear on each die=6^6
so the probability required=6!/(6^6)=5!/(6^5)=(5*4*(3*2))/(6*6*6*6*6)=5/(9*6*6)
=5/324...

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jayesh damani  (11 years ago)

Imagine you throw one after the other. You consider a throw as a success if the number is different from all previous numbers. You start with one. This is always a succes so P(first)=1=66. Your second throw is a success if one of the remaining 5 numbers shows, so P(second)=56. And so on. Since all the throws are independent, the total probability is the product of all separate probabilities:


P(all numbers are different)=6/6⋅5/6⋅4/6⋅3/6⋅2/6⋅1/6

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