Worked solution
Seat three people in ten seats without replacement
There are 10 vacant seats in a bus. In how many ways can 3 people seat themselves?
CJC · Lecture · Example 4
Use the first three seat-choice stages
| Person | 1st | 2nd | 3rd |
|---|---|---|---|
| Available seats | 10 | 9 | 8 |
There are 10 choices for the first person,9 for the second and 8 for the third.
How did this part go?
Recognise an ordered selection
Number of ways=. We choose seats for three distinct people; changing who occupies a seat changes the outcome.
How did this part go?
Evaluate nPr on the source calculator
Type 10 in the main screen; press MATH, select PROB, then 2:nPr; type 3 and press ENTER. The source display 10 nPr 3 returns 720. The last step and display continue from printed page 4 onto page 5.
How did this part go?
Common mistakes
Choosing an unordered set of three seats is not enough: the three people can occupy each chosen set in 3! different ways.