There are 5 freshmen, 8 sophomores, and 7 juniors in a chess club. A group of 6 students will be chosen to compete in a competition.

1.

How many combinations of students are possible if the group is to consist of exactly 3 freshmen

Question

There are 5 freshmen, 8 sophomores, and 7 juniors in a chess club. A group of 6 students will be chosen to compete in a competition.


1.
 

How many combinations of students are possible if the group is to consist of exactly 3 freshmen

kropot72 · Answer

The number of combinations of 5 freshmen taken 3 at a time is 5C3. Each of these combinations can be taken with each of the 17C3 combinations of the remaining students. Therefore the required number of combinations is given by:
5C3 * 17C3