Difference between revisions of "2015 AIME I Problems/Problem 5"
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In a drawer Sandy has <math>5</math> pairs of socks, each pair a different color. On Monday Sandy selects two individual socks at random from the <math>10</math> socks in the drawer. On Tuesday Sandy selects <math>2</math> of the remaining <math>8</math> socks at random and on Wednesday two of the remaining <math>6</math> socks at random. The probability that Wednesday is the first day Sandy selects matching socks is <math>\frac{m}{n}</math>, where <math>m</math> and <math>n</math> are relatively prime positive integers, Find <math>m+n</math>. | In a drawer Sandy has <math>5</math> pairs of socks, each pair a different color. On Monday Sandy selects two individual socks at random from the <math>10</math> socks in the drawer. On Tuesday Sandy selects <math>2</math> of the remaining <math>8</math> socks at random and on Wednesday two of the remaining <math>6</math> socks at random. The probability that Wednesday is the first day Sandy selects matching socks is <math>\frac{m}{n}</math>, where <math>m</math> and <math>n</math> are relatively prime positive integers, Find <math>m+n</math>. | ||
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+ | == See also == | ||
+ | {{AIME box|year=2015|n=I|num-b=1|num-a=3}} | ||
+ | {{MAA Notice}} | ||
+ | [[Category:Introductory Geometry Problems]] |
Revision as of 12:25, 20 March 2015
Problem
In a drawer Sandy has pairs of socks, each pair a different color. On Monday Sandy selects two individual socks at random from the socks in the drawer. On Tuesday Sandy selects of the remaining socks at random and on Wednesday two of the remaining socks at random. The probability that Wednesday is the first day Sandy selects matching socks is , where and are relatively prime positive integers, Find .
See also
2015 AIME I (Problems • Answer Key • Resources) | ||
Preceded by Problem 1 |
Followed by Problem 3 | |
1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 | ||
All AIME Problems and Solutions |
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