Difference between revisions of "2017 AIME II Problems/Problem 9"
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| − | + | ==Problem== | |
A special deck of cards contains <math>49</math> cards, each labeled with a number from <math>1</math> to <math>7</math> and colored with one of seven solors. Each number-color combination appears on exactly one card. Sharon will select a set of eight cards from the deck at random. Given that she gets at least one card of each color and at least one cardf with each number, the probability that Sharon can discard one of her cards and <math>\textit{still}</math> have at least one card of each color and at least one card with each number if <math>\frac{p}{q}</math>, where <math>p</math> and <math>q</math> are relatively prime positive integers. Find <math>p+q</math>. | A special deck of cards contains <math>49</math> cards, each labeled with a number from <math>1</math> to <math>7</math> and colored with one of seven solors. Each number-color combination appears on exactly one card. Sharon will select a set of eight cards from the deck at random. Given that she gets at least one card of each color and at least one cardf with each number, the probability that Sharon can discard one of her cards and <math>\textit{still}</math> have at least one card of each color and at least one card with each number if <math>\frac{p}{q}</math>, where <math>p</math> and <math>q</math> are relatively prime positive integers. Find <math>p+q</math>. | ||
| − | + | ==Solution== | |
<math>\boxed{013}</math> | <math>\boxed{013}</math> | ||
| + | |||
| + | =See Also= | ||
| + | {{AIME box|year=2017|n=II|num-b=8|num-a=10}} | ||
| + | {{MAA Notice}} | ||
Revision as of 12:55, 23 March 2017
Problem
A special deck of cards contains 
cards, each labeled with a number from 
to 
and colored with one of seven solors. Each number-color combination appears on exactly one card. Sharon will select a set of eight cards from the deck at random. Given that she gets at least one card of each color and at least one cardf with each number, the probability that Sharon can discard one of her cards and 
have at least one card of each color and at least one card with each number if 
, where 
and 
are relatively prime positive integers. Find 
.
Solution
See Also
| 2017 AIME II (Problems • Answer Key • Resources) | ||
| Preceded by Problem 8 |
Followed by Problem 10 | |
| 1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 | ||
| All AIME Problems and Solutions | ||
The problems on this page are copyrighted by the Mathematical Association of America's American Mathematics Competitions. 
