1993 AIME Problems/Problem 7

Problem

Three numbers, $a_1\,$ , $a_2\,$ , $a_3\,$ , are drawn randomly and without replacement from the set $\{1, 2, 3, \dots, 1000\}\,$ . Three other numbers, $b_1\,$ , $b_2\,$ , $b_3\,$ , are then drawn randomly and without replacement from the remaining set of 997 numbers. Let $p\,$ be the probability that, after a suitable rotation, a brick of dimensions $a_1 \times a_2 \times a_3\,$ can be enclosed in a box of dimensions $b_1 \times b_2 \times b_3\,$ , with the sides of the brick parallel to the sides of the box. If $p\,$ is written as a fraction in lowest terms, what is the sum of the numerator and denominator?

Solution

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1993 AIME (Problems • Answer Key • Resources)
Preceded by Problem 6	Followed by Problem 8
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1993 AIME Problems/Problem 7

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