1997 AJHSME Problems/Problem 9
Contents
[hide]Problem
Three students, with different names, line up single file. What is the probability that they are in alphabetical order from front-to-back?
Solution 1
There are ways to pick the first student, ways to pick the second student, and way to pick the last student, for a total of ways to line the students up.
Only of those ways is alphabetical. Thus, the probability is or
Solution 2
Give the students uncreative names like Abby Adams, Bob Bott, and Carol Crock: , , and , replacing the alphabetically first student's name with , and the alphabetically last student's name with . List all the ways they can line up:
Only of those lists is in alphabetical order, giving an answer of or
See also
1997 AJHSME (Problems • Answer Key • Resources) | ||
Preceded by Problem 8 |
Followed by Problem 10 | |
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All AJHSME/AMC 8 Problems and Solutions |
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