A deck of cards is shuffled and then divided into two piles of 26 cards each....

A deck of cards is shuffled and then divided into two piles of 26 cards each. We say that a suit

is unsplit if all 13 cards of that suit are in the same pile. Compute the probability that at least one suit will be unsplit.

Solutions

Expert Solution

ANSWER::

The number of ways in which cards can be distributed so that there is one unsplit suit

where is the number of ways of selecting one suit from the 4, and is the number of ways of selecting 26 cards from the rest of the 39 cards made by the three suits that are left.

Now, in selecting 26 from rest of the 39 cards, we are making those selections too in which there will be two suits unsplit and 4 suits unsplit (there is no 3 suits unsplit since it is the same as 4 suits unsplit).

Hence, the total number of ways of distributing the cards so that there is at least one suit unsplit

The total number of ways of distributing the cards into two piles

So, the probability that at least one suit will be unsplit

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orchestra answered 1 year ago

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