Combinations Question (Please provide an explanation!)

Question

1. There are 140 students in the entire 12th Grade class.
2. 52 signed up for biology.
3. 71 signed up for chemistry.
4. 40 signed up for physics.
5. 15 signed up for biology and chemistry
6. 8 signed up for chemistry and physics.
7. 11 signed up for biology and physics.
8. 2 signed up for all 3 sciences.

a) How many students are NOT taking any science?

The answer for a) is 9, why is that? Explain if can.

b) Illustrate this using a Venn diagram.

Please provide an explanation, I don't understand.

Answer 1

In the intersection of all three circles put 2 (for those taking all three)

In the intersection of B and P put 9 (11 - 2 that are in all three)

In the intersection of B and C put 13 (15 - 2 that are in all three)

In the intersection of C and P put 6 (8 - 2 that are in all three)

In B put 28 (52 - 9 - 2 - 13)

In C put 50 (71 - 13 - 2 - 6)

In P put 23 (40 - 9 - 2 - 6)

Add all of the numbers and you get 131 which is 9 less than the 140 in the school.

Now use this model to solve your other post.

Answer 2

Let me know if you have any further questions and please leave a rating. Goodluck!