Lorena Beard

2022-07-15

Five people are going to be seated in a row of seven chairs. How many different ways can they be seated?

Camron Herrera

Expert

Step 1
There are $_7{C}_{5}=\frac{7!}{5!\cdot 2!}=21$ ways of choosing which 5 chairs from the 7 will have people sitting in them.
Step 2
For each of these ways there are:
5 ways to pick the first person;
4 ways to pick the second person;
etc. f or $5!=120$ ways of arranging the people in the chosen seats.
Therefore there are $\text{XXX}21×120=2520$ ways of making this seating

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