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  • A deck of 52 playing cards is randomly shuffled. What is the probability that the cards are in the exact order of a previously sorted deck?  <div class

A deck of 52 playing cards is randomly shuffled. What is the probability that the cards are in the exact order of a previously sorted deck?

 

Option: 1

\mathrm{1 / 32 ! }


Option: 2

1 / 12 !


Option: 3

1 / 52 !


Option: 4

1 / 42 !


Answers (1)

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The probability of the cards being in the exact order of a previously sorted deck depends on the number of possible permutations of the 52 cards and the total number of possible arrangements of the cards.

There is only one specific order that matches the previously sorted deck, and this order can be considered as one successful outcome. The total number of possible arrangements of the 52 cards is given by 52 !.
Therefore, the probability is:

1 / 52 !
However, 52 ! is an extremely large number, approximately equal to 8.0658 \times 10^{\wedge} 67. As a result, the probability of the cards being in the exact order of a previously sorted deck is exceedingly low.

Posted by

Divya Prakash Singh

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