Worked solution
Seat ten distinct people in ten distinct seats
There are 10 vacant seats in a bus. In how many ways can 10 people seat themselves?
CJC · Lecture · Example 3
Use one seat choice for each successive person
Each person and seat is distinct, and a chosen seat is no longer available.
| Person | 1st | 2nd | 3rd | 4th | 5th | 6th | 7th | 8th | 9th | 10th |
|---|---|---|---|---|---|---|---|---|---|---|
| Available seats | 10 | 9 | 8 | 7 | 6 | 5 | 4 | 3 | 2 | 1 |
How did this part go?
Multiply all ten stages
Number of ways=. Swapping two people gives a different seating arrangement.
How did this part go?
Evaluate the factorial on the source calculator
On the graphing calculator shown in the notes: type 10 in the main screen; press MATH, select PROB, then 4:!; press ENTER. The input 10! returns 3628800. These are the source menu steps; the multiplication explains the count.
How did this part go?
Common mistakes
Seats are distinct positions. Do not divide by 10! after counting: the identities of the people and their seats matter.