Question

Bob is planning to pack 6 shirts and 4 pairs of pants for a trip. If he has 8 shirts and 7 pairs of pants to choose from, in how many different ways can this be done?

Answer 1

As the order of selection of shirts does not matter, number of different ways Bob can select 6 shirts from 8 shirts is

8C6 = 8! / ((8-6)! 6!) = 8! / (2! 6!)  

= (8 * 7) / (2 * 1)

= 28

As the order of selection of pairs of pants does not matter, number of different ways Bob can select 4 pairs of pants from 7 is

7C4 = 7! / ((7-4)! 4!) = 7! / (3! 4!)  

= (7 * 6 * 5) / (3 * 2 * 1)

= 35

Number of different ways to pack 6 shirts and 4 pairs of pants for a trip is,

28 * 35 = 980