Mel J.

asked • 05/08/21# Combinations Question (Please provide an explanation!)

- There are 140 students in the entire 12th Grade class.
- 52 signed up for biology.
- 71 signed up for chemistry.
- 40 signed up for physics.
- 15 signed up for biology and chemistry
- 8 signed up for chemistry and physics.
- 11 signed up for biology and physics.
- 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.**

## 2 Answers By Expert Tutors

Mark M. answered • 05/08/21

Mathematics Teacher - NCLB Highly Qualified

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.

Mel J.

Thank you!05/08/21

Eli H. answered • 05/08/21

Experienced tutor in Physics, Calculus, Algebra, and ACT/SAT Math

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

Mel J.

Thank you so much, your video was very helpful! I really appreciate the help.05/08/21

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Mark M.

Have you examined any examples of problems solved with Venn Diagrams?05/08/21