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

1 Answer
Oct 13, 2016

Answer:

#color(green)(2520)#

Explanation:

There are #_7C_5 = (7!)/(5! * 2!) = 21# ways of choosing which #5# chairs from the #7# will have people sitting in them.

For each of these ways there are:
#color(white)("XXX")5# ways to pick the first person;
#color(white)("XXX")4# ways to pick the second person;
#color(white)("XXX")etc. for #5!=120# ways of arranging the people in the chosen seats.

Therefore there are
#color(white)("XXX")21xx120=2520# ways of making this seating