Question 11

Explanation

Identifying the Concept

This problem asks us to select team members based on their expertise. Since the order of selection does not matter (who is chosen first or second does not change the team composition), we use the concept of Combination.

The combination formula is:

Calculating Mathematician Combinations

From $3$ mathematicians, $2$ will be chosen:

Calculating Physicist Combinations

From $5$ physicists, $3$ will be chosen:

Calculating Total Ways

Since the selection of mathematicians and physicists are independent events occurring together, we multiply the two results:

Thus, there are $30$ ways to form the team.