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How many distinct ways are there of ordering a deck of 52 cards such that all hearts occur before any other card? (that is, the first 13 cards are all hearts?
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How many distinct ways are there of ordering a deck of 52 cards such that all hearts occur before any other card? (that is, the first 13 cards are all hearts?

User Proninyaroslav
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1 Answer

5 votes
The first 13 cards (all hearts) have
13! ways of being arranged. The remaining 39 have
39! ways of being arranged.

The total number of such arrangements is then
13!39!, or about
1.27*10^(56) arrangements.
User Nourah
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7.6k points
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