The product rule for counting
The Maths Habit
List them all.
Pairs picked from A, B, C and D
AB, AC, AD, BC, BD, CD2 digit numbers from 4, 7 and 0. No 0 first.
40, 47, 70, 74Codes: X or Y, then 1, 2 or 3
X1, X2, X3, Y1, Y2, Y3
A padlock has 3 dials. Each dial shows 0 to 9.
How long would it take to try every code?
1000 codes: about 33 minutes at 2 seconds each
An ice cream is one flavour (A to D) and one topping (1 to 6).
| 1 | 2 | 3 | 4 | 5 | 6 | |
|---|---|---|---|---|---|---|
| A | A1 | A2 | A3 | A4 | A5 | A6 |
| B | B1 | B2 | B3 | B4 | B5 | B6 |
| C | C1 | C2 | C3 | C4 | C5 | C6 |
| D | D1 | D2 | D3 | D4 | D5 | D6 |
Each ice cream is one square. How many are there? 24
An ice cream is one flavour (A to D) and one topping (1 to 6).
| 1 | 2 | 3 | 4 | 5 | 6 | ||
|---|---|---|---|---|---|---|---|
| A | 6 | ||||||
| B | 6 | ||||||
| C | 6 | ||||||
| D | 6 |
4 rows, 6 in each row: 4 × 6 = 24
An ice cream is one flavour (A to D) and one topping (1 to 6).
The quick way: no grid, just multiply the choices.
- Product rule
- Multiply the number of choices at each step.
How many outcomes?
There are 5 starters and 6 mains. How many two-course meals are there?
A code is 2 digits, each from 0 to 9. How many codes are there?
There are 5 starters and 6 mains. How many two-course meals are there?
In how many orders can 3 people stand in a line?
There are 5 starters and 6 mains. How many two-course meals are there?
Ice cream comes in 8 flavours, in a cone or a tub. How many different choices are there?
There are 5 starters and 6 mains. How many two-course meals are there?
Mia reads one book from a shelf of 9 on Monday, and a different one on Tuesday. In how many ways can she choose?
There are 5 starters and 6 mains. How many two-course meals are there?
A dice is rolled, a coin is flipped and a spinner numbered 1 to 4 is spun. How many outcomes are there?
Answer sheet
How many 3-digit even numbers can be made from 1, 2, 3, 4 and 5 with no digit repeated?
24Two different students are picked from 20. The order does not matter. How many pairs are there?
190
A mug comes in 4 colours and 7 designs. How many different mugs are there?
28A code is 3 letters from A to F. Letters can repeat. How many codes are there?
216Five runners finish a race. In how many ways can first, second and third place be filled?
60