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?
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
