Five people are going to be seated in a row of seven chairs. How many...

Lorena Beard

Lorena Beard

Answered

2022-07-15

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

Answer & Explanation

Camron Herrera

Camron Herrera

Expert

2022-07-16Added 16 answers

Step 1
There are _ 7 C 5 = 7 ! 5 ! 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 XXX 21 × 120 = 2520 ways of making this seating

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