Question

Our class is creating a new academic team, the Data Managers. The team will have 4 members to perform different tasks: collector, analyser, grapher, and recorder. 10 people in class want to be on the team, so we pick a random team out of the 10.

If exactly 4 boys volunteer, what is the probability that the team is all boys or no boys? Evaluate your answer.
What is the probability that Student 1 and Student 2 are on the team? Evaluate your answer.
With two teacher coaches, the team of four takes a picture (6 people in picture). What is the probability that the teachers are together in the picture? Evaluate your answer.

Answer 1

A) 16/210

B) 2/15

C) 1/3

Explanation:

Since a random team of ten is picked and that the team will have 4 members to perform different tasks. Thus;

Number of ways to select the team = 10C4 = 10!/(4! × 6!) = 210

A) If exactly 4 boys volunteer, probability that the team is all boys or no boys

For all boys; P = (4C4 × 6C0)/210 = (1 × 1)/210 = 1/210

For no boys; P = (4C0 × 6C4) /210 = (1 × 15)/210 = 15/210

Thus, probability that the team is all boys or no boys = (1/210) + (15/210) = 16/210

B) probability that Student 1 and Student 2 are on the team = (8C2/10C4) = 28/210 = 2/15

C) probability that the teachers are together in the picture = (5! × 2!)/6! = 1/3

This because we considered the two teacher coaches to be one unit.