Difference between revisions of "2015 AIME I Problems/Problem 5"

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==Problem==
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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>.

Revision as of 11:57, 20 March 2015

Problem

In a drawer Sandy has $5$ pairs of socks, each pair a different color. On Monday Sandy selects two individual socks at random from the $10$ socks in the drawer. On Tuesday Sandy selects $2$ of the remaining $8$ socks at random and on Wednesday two of the remaining $6$ socks at random. The probability that Wednesday is the first day Sandy selects matching socks is $\frac{m}{n}$, where $m$ and $n$ are relatively prime positive integers, Find $m+n$.

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