From a group of 15 people, how many ways are there to select 5​ people to receive $50​ gift certificates?

A customer at a bookstore is choosing four paperback novels to take on a trip, from a shelf containing 42 books. How many different combinations of books are there ?

In a 10 team tournament, trophies are to be given to the top 3 places. In how many ways can the trophies be awarded?

A school club has 25 members and needs to elect four officers: a president, vice-president, secretary, and treasurer. How many ways can this be done?

At the Harris Burger Bar each customer designs their own burger by choosing: one from two types of bun, one from three types of filling, and two different side dishes from six available. How many different burgers can be created?

There are 30 people competing in a race. The top 3 get a spot on the podium. How many different ways can you choose 3 out of 30?

Your sister is shopping at an exclusive Rodeo Drive clothing store and examines 4 distinct blouses, 5 distinct dresses, and 2 distinct handbags. How many different combinations of items can she purchase if she buys exactly 2 blouses, 3 dresses and 1 handbag?

How many $30 tickets were sold?

At a school meeting, 78 handshakes took place. Each person shook hands exactly ​ once with each of the others present. How many people were at the school meeting?

The math club wants to choose a committee to plan the back to school party. How many 5 person committees can be formed from the set of 20 members?