Question

A box contains five cards, numbered 1, 2, 3, 4, and 5. Three cards are selected randomly without replacement from the box. What is the probability that 4 is the largest value selected?

$\dfrac{1}{10}$

$\dfrac{1}{5}$

$\dfrac{3}{10}$

$\dfrac{2}{5}$

$\dfrac{1}{2}$

Answer: C

Concepts:basic probability combinations

Difficulty rating: 1020

Video solution:

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Written solution:

The number of ways to choose $3$ cards from $5$ is ${5 \choose 3} = 10.$ If $4$ is the largest value selected, then the other two cards have to be chosen from $\{1, 2, 3\}.$ There are ${3 \choose 2} = 3$ ways to do this. The probability is then $\dfrac{3}{10}.$

Thus, C is the correct answer.

2017 AMC 8 Problem 10

Answer: C

Difficulty rating: 1020

Video solution:

Written solution:

Problem 10 in Other Years