There are 36 cards labeled with the numbers 1 through 36 and then placed face down on a table. If four cards are revealed one after the other, what is the probability that each card’s number is larger than the last?
For example, one such sequence of cards is 3, 15, 17, 33.
The probability is 1⁄24 ≈ 4.2 percent.
Having drawn any four cards, there are 24 different possible orders they can appear in, as calculated below:
4! = 4 × 3 × 2 × 1 = 24
Only one of these 24 sequences fulfills the condition that the numerical values drawn one after the other become larger. Because all 36 cards are labeled differently, the number of cards is unimportant for the solution.
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This puzzle originally appeared in Spektrum der Wissenschaft and was reproduced with permission.