1997 AJHSME Problems/Problem 9
Revision as of 14:45, 31 July 2011 by Talkinaway (talk | contribs) (Created page with "==Problem== Three students, with different names, line up single file. What is the probability that they are in alphabetical order from front-to-back? <math>\text{(A)}\ \dfrac{...")
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: ,
, 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 |