Question

In a hat containing 7 names of players in a tennis squad, including the captain and vice-captain, what is the probability of randomly selecting a team of 3 players that does not include the captain or vice-captain?

A) 3/21
B) 12/21
C) 15/21
D) 18/21

Answer 1

The probability of randomly selecting a team of 3 players that does not include the captain or vice-captain is 2/7.

Step-by-step explanation:

To find the probability of randomly selecting a team of 3 players that does not include the captain or vice-captain, we need to determine the number of favorable outcomes and the total number of possible outcomes.

There are 5 players left in the hat after the captain and vice-captain are excluded. The number of ways to choose 3 players from these 5 is given by the combination formula: C(5, 3) = 5! / (3!(5-3)!) = 10.

Since there are 7 players in total, the total number of possible outcomes is given by the combination formula: C(7, 3) = 7! / (3!(7-3)!) = 35.

Therefore, the probability of randomly selecting a team of 3 players that does not include the captain or vice-captain is 10/35, which simplifies to 2/7.