Difference between revisions of "1997 AJHSME Problems/Problem 9"
m (→Solution 2) |
|||
| Line 12: | Line 12: | ||
==Solution 2== | ==Solution 2== | ||
| − | Give the students uncreative names: <math>A</math>, <math>B</math>, and <math>C</math>, replacing the alphabetically first student's name with <math>A</math>, and the alphabetically last student's name with <math>C</math>. List all the ways they can line up: | + | Give the students uncreative names like Abby Adams, Bob Bott, and Carol Crock: <math>A</math>, <math>B</math>, and <math>C</math>, replacing the alphabetically first student's name with <math>A</math>, and the alphabetically last student's name with <math>C</math>. List all the ways they can line up: |
<math>ABC</math> | <math>ABC</math> | ||
Latest revision as of 18:54, 23 October 2015
Contents
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 | |
| 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 | ||
| All AJHSME/AMC 8 Problems and Solutions | ||
The problems on this page are copyrighted by the Mathematical Association of America's American Mathematics Competitions. 
