Answer:
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.