A café offers 4 sandwiches, 3 soups and 2 drinks. A lunch is one… Step by Step

Step by step

The question

Question: There are 4 sandwiches, 3 soups and 2 drinks.

How many lunches can be made with one of each?

There are four choices.

First we solve it, the normal way.

Then we pick.

1 Count the choices

First we choose one of the sandwiches: 4 choices.

Then one of the soups: 3 choices.

Then one of the drinks: 2 choices.

2 Multiply

Every choice goes with every other choice.

So we multiply them all: 4 × 3 × 2.

lunches = 4 × 3 × 2

This is the counting principle: multiply the number of choices.

counting principle:

multiply the choices

Careful!

We do not add the choices: 4 plus 3 plus 2 is only 9.

Every choice goes with every other one, so we multiply.

Careful: not 4 + 3 + 2 = 9 ✗

4 times 3 is 12.

12 times 2 is 24.

4 × 3 = 12

12 × 2 = 24

So there are 24 lunches.

lunches = 24

3 Check

Let's check in another order.

First 3 times 2 is 6.

3 × 2 = 6

Then 4 times 6 is 24.

The same.

So the answer is right!

4 × 6 = 24

4 Pick the choice

Our answer is lunches = 24.

That is choice D.

D) 24

5 Why not the others

A is 6.

Wrong: 3 × 2: forgot the sandwiches.

A) 6 ✗ 3 × 2: forgot the sandwiches

B is 9.

Wrong: 4 + 3 + 2: added; for each sandwich there are 3 soups, so we multiply.

That is the Careful mistake from before.

B) 9 ✗ 4 + 3 + 2: added; for each sandwich there are 3 soups, so we multiply

C is 12.

Wrong: 4 × 3: forgot the drinks.

C) 12 ✗ 4 × 3: forgot the drinks

Let's look back.

First: count the choices.

Then: multiply.

Then: check.

Then: pick the choice.

Last: why not the others.

Answer