Question

You volunteer to help drive people home from an event. There are 18 people who need rides, but you can only fit 7 of them in your vehicle. How many different groups of 7 people can you drive?

Answer 1

18 choose 7 
=C(18,7)
=18!/(7!(18-7)!)
=31824
OR
18 choices for first passenger,
17 choices for second passenger,
....
12 choices for 7th passenger,
so total = 18*17*16...12
but there are 7! ways to order the 7 passengers, so
number of groups
=18*17*16...12/7!
=31824   as well