Question

A box of jerseys for a pick-up game of basketball contains 10 extra-large jerseys, 7 large jerseys, and 5 medium jerseys. If you are first to the box and grab 3 jerseys, what is the probability that you randomly grab 3 medium jerseys? Express your answer as a fraction in lowest terms or a decimal rounded to the nearest millionth.

Answer 1

First, we find the total number of ways to choose 3 jerseys out of the total number of jerseys available:

Total number of jerseys = 10 + 7 + 5 = 22 jerseys

Number of ways to choose 3 jerseys out of 22 jerseys = 22 choose 3 = 22! / (3!(22-3)!) = 22! / (3! * 19!) = 1540

Next, we find the number of ways to choose 3 medium jerseys out of the 5 medium jerseys available:

Number of medium jerseys = 5

Number of ways to choose 3 medium jerseys out of 5 medium jerseys = 5 choose 3 = 5! / (3!(5-3)!) = 5! / (3! * 2!) = 10

Therefore, the probability of randomly grabbing 3 medium jerseys out of the total number of jerseys is:

Probability = Number of ways to choose 3 medium jerseys / Total number of ways to choose 3 jerseys
Probability = 10 / 1540
Probability ≈ 0.00649

So, the probability of randomly grabbing 3 medium jerseys is approximately 0.00649.