1997 AMC 8 Problem 9
Attempt Problem 9 of the 1997 AMC 8 below, then check your answer against the professionally curated solution from LIVE by Po-Shen Loh. You can also try the full timed exam, view all 1997 AMC 8 solutions, or check the answer key.
All problems are used with official legal permission of the Mathematical Association of America (MAA).
9.
Three students, with different names, line up single file. What is the probability that they are in alphabetical order from front-to-back?
Answer: C
Small hint:
Only one ordering is alphabetical
Big hint:
Count all possible orders of the three students
Solution:
There are options for the person in front. Then, there are options for the person in the middle.
This leaves choice for the person at the end. There are ways for the people to line up.
Only one of these lines is correct, and the probability it occurs is
Thus, C is the correct answer.
Problem 9 in other years
- 1985 AMC 8
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