Our club has 10 members, and we need to appoint a president, a vice-president, and a secretary. How many ways can we do this if members can hold any number of offices?
If a person could only have at most 1 office at a time, then we would be "choosing" 3 people from the 10. This is why tmatthews answered \(\binom{10}{3}\). However, since a person can have more than one office, then there are 10 options for the President, 10 for the vice President, and 10 for the secretary. This gets us 10 x 10 x 10 = 1000.
