2005 AMC 10A Problem 9

Question

Three tiles are marked X and two other tiles are marked O. The five tiles are randomly arranged in a row. What is the probability that the arrangement reads XOXOX?

\dfrac{1}{12}

\dfrac{1}{10}

\dfrac{1}{6}

\dfrac{1}{4}

\dfrac{1}{3}

Answer: B

Concepts:basic probability combinations

Difficulty rating: 1280

Small hint:

Count the distinct arrangements of three X’s and two O’s in a row

Big hint:

The two O’s occupy

\binom{5}{2}

equally likely position sets, and only one of them gives XOXOX

Solution:

The three X positions can be any of

\binom{5}{3} = 10

equally likely choices, and exactly one of them produces XOXOX. So the probability is

\dfrac{1}{10}.

Thus, the correct answer is B.