Question

It’s a new semester! Students are grouped into three clubs, which each has 10, 4 and 5 students. In how many ways can teacher select 2 students from all these clubs so they are from different clubs?

Answer 1

Here we must see in how many different ways we can select 2 students from the 3 clubs, such that the students do not belong to the same club. We will see that there are 110 different ways in which 2 students from different clubs can be selected.

So there are 3 clubs:

• Club A, with 10 students.
• Club B, with 4 students.
• Club C, with 5 students.

The possible combinations of 2 students from different clubs are

• Club A with club B
• Club A with club C
• Club B with club C.

The number of combinations for each of these is given by the product between the number of students in the club, so we get:

• Club A with club B: 10*4 = 40
• Club A with club C: 10*5 = 50
• Club B with club C. 4*5 = 20

For a total of 40 + 50 + 20 = 110 different combinations.

This means that there are 110 different ways in which 2 students from different clubs can be selected.

If you want to learn more about combination and selections, you can read:

brainly.com/question/251701