Worked examples
Two examples
Example 1
8 runners race. In how many ways can first, second and third be filled?
- 8 choices for first, then 7, then 6: 8 × 7 × 6.
Answer: 336
Example 2
In how many orders can 5 people stand in a line?
- 5 × 4 × 3 × 2 × 1.
Answer: 120
Where this is taught: Quiz 34: Probability and Counting, “When the order matters, and when it does not”
The drill
Ten problems
How many:
Type each answer, then press Check my answers at the bottom. Commas in large numbers are fine.Write each answer on the line. The answer key, with the reasoning, is on the last page.