Integers from 1 through 100 are written on a hundred cards. The deck is properly shuffled, and 3 cards are drawn at random.
What is the probability that the cards are drawn in increasing order?
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For any 3 cards there are 3 ! = 6 orders in which they can be picked, only one of which is in ascending order. Since each of these orders is equally likely, the desired probability is 6 1 .