Practice Question 11.1.2
There are 13 people in a race. How many ways can the 13 runners cross the finish line?
Answer to Practice Question 11.1.2
- There are 13 different contestants who can place 1st.
- There are 12 different contestants who can place 2nd (all but the 1st place contestant).
- There are 11 different contestants who can place 3rd (all but the 1st and 2nd place contestants).
- There are 10 different contestants who can place 4th (all but the 1st, 2nd, and 3rd place contestants).
- There are 9 different contestants who can place 5th (all but the 1st, 2nd, 3rd, and 4th place contestants).
- There are 8 different contestants who can place 6th (all but the 1st - 5th place contestants).
- There are 7 different contestants who can place 7th (all but the 1st - 6th place contestants).
- There are 6 different contestants who can place 8th (all but the 1st - 7th place contestants).
- There are 5 different contestants who can place 9th (all but the 1st - 8th place contestants).
- There are 4 different contestants who can place 10th (the last 4 runners).
- There are 3 different contestants who can place 11th (the last 3 runners).
- There are 2 different contestants who can place 12th (the last 2 runners).
- There is only 1 contestant who can place 13th (the last runner).
Using the Fundamental Counting Rule, there are
\[13\times 12\times 10\times 9\times 8\times 7\times 6\times 5\times 4\times 3\times 2\times 1 = \mathbf{6,227,020,800}\]
possible ways the 13 contestants can cross the finish line.