Foundation and Higher · counting outcomes

How many ways?
List them, or
just multiply.

the product rule
for counting

listing without missing any —

Systematic

fix the first choice,

change the last one in order

step 1 of 4

List in order

1. Hold the red top. Try every bottom.

2. Then the blue top, same order.

✓ Working in order misses none

tops: R, Bbottoms: J, S, T

RJRSRT

BJBSBT

6 outfits

step 2 of 4

The product rule

1. Multiply the number of choices.

2. It matches the list: 2 rows of 3.

✓ Choices × choices

2 tops, 3 bottoms

2 × 3 = 6

each top pairs with all 3

step 3 of 4

Three choices

1. Too many to list. Multiply all three.

2. 3 × 5 = 15, then 15 × 2 = 30.

✓ One number for each choice made

3 starters, 5 mains, 2 desserts

3 × 5 × 2

= 30 different meals

step 4 of 4 · Higher

No repeats

1. 4 choices for the first letter.

2. One is used up: 3 left, then 2.

✓ With repeats: 4 × 4 × 4 = 64

3-letter codes from A, B, C, D, no repeats

4 × 3 × 2 one fewer each time

= 24 codes

counting outcomes —

List

fix one, change the other in order

Product rule

multiply the choices

No repeats

one fewer each time

“How many ways” usually
means multiply.

The
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