3 Card Shuffle

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?

3 100 \frac{3}{100} 1 8 \frac{1}{8} 1 3 \frac{1}{3} 1 6 \frac{ 1}{6}

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1 solution

For any 3 3 cards there are 3 ! = 6 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 1 6 \boxed{\dfrac{1}{6}} .

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