1986 AHSME Problems/Problem 22
Problem
Six distinct integers are picked at random from . What is the probability that, among those selected, the second smallest is ?
Solution
The total number of ways to choose 6 numbers is .
Assume is the second-lowest number. There are numbers left to choose, of which must be greater than , and of which must be less than . This is equivalent to choosing numbers from the numbers larger than , and number from the numbers less than .
Thus, , which is .
See also
1986 AHSME (Problems • Answer Key • Resources) | ||
Preceded by Problem 21 |
Followed by Problem 23 | |
1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 • 16 • 17 • 18 • 19 • 20 • 21 • 22 • 23 • 24 • 25 • 26 • 27 • 28 • 29 • 30 | ||
All AHSME Problems and Solutions |
The problems on this page are copyrighted by the Mathematical Association of America's American Mathematics Competitions.