### math problem # 8

**Group Members:**

Thyrza May

Julie Rose

Michael

Alex M.

Rina

Cindy

**Problem:**

Jason Jolt is lending part of his art collection to the local library. He has 5 oil paintings and 2 watercolors. The library would like to borrow two oil paintings and one watercolor. In how many different ways can Jason choose the three paintings?

**Answer:**

Answer:This question is like number 6. You list all the possibilities. To make it easier, pretend the six oil paints are A, B, C, D and E . Also pretend the two water color as 1 and 2. Just like shown below but be careful because you shouldn't have same posibilities like A, B, 1 and B, A, 1 because it is the same the order doesn't matter.Oil Paintings:A, B, C, D, EWater Color:1, 2

Here are the Posibilities:

A, B ,1

A, C, 1

A, D, 1

A, E, 1

A, B, 2

A, C, 2

A, D, 2

A, E, 2

B, C, 1

B, D, 1

B, E, 1

B, C, 2

B, D, 2

B, E, 2

C, D, 1

C, E, 1

C, E, 2

C, D, 2

D, E, 1

D, E, 2

* THERE ARE 20 DIFFERENT WAYS OF CHOOSING THE THREE PAINTINGS *

Shortcut:

Try to solve the posibilities with only one water color. Like this:

A, B ,1

A, C, 1

A, D, 1

A, E, 1

B, C, 1

B, D, 1

B, E, 1

C, D, 1

C, E, 1

D, E, 1

So there's 10 posibilities but don't forget there's two water colors. So you multiply the answer to 2 and in this case it is ten . So you multiply 10 by two which is 20.

* THERE ARE 20 DIFFERENT WAYS OF CHOOSING THE THREE PAINTINGS *

## 1 Comments:

Now this is a perfect answer to this question. You showed the detailed breakdown and then came up with an ingenious shortcut to help solve the problem quicker in the future.

Nice job!

Mr. R

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