# Thread: Selecting a team under restriction.

1. ## Selecting a team under restriction.

A team of 11 students is chosen randomly from a class of 40 students for a sports event. In the past two years, 15 of these 40 students have participated in this event at least once. What is the probability of selecting for the team at least 3 but no more than 5 students from the group of 15 that have previously participated?

2. Originally Posted by davery
A team of 11 students is chosen randomly from a class of 40 students for a sports event. In the past two years, 15 of these 40 students have participated in this event at least once. What is the probability of selecting for the team at least 3 but no more than 5 students from the group of 15 that have previously participated?
The number of teams that satisfy the restriction is $\displaystyle {15 \choose 3} \cdot {25 \choose 8} + .... + {15 \choose 5} \cdot {25 \choose 6} = .....$

You should know what to with this number. If you need more help, please show all your work and say where you get stuck.