102. Deck of Cards. The cards in the deck are sequentially numbered from 1 to 7, and then thoroughly shuffled. Five cards are randomly drawn sequentially from the deck. What is the probability that the numbers on these cards will be in increasing order?
102. We are only interested in the order of the drawn cards. There are 5! permutations of five numbers in total; therefore, the desired probability is $\frac{1}{120}$.

[ Дж. Р. Ziegler, M. M., 23, 278 (May 1950).]

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