How many unique 3 digit codes can be created from the 5 digits {1, 2, 3, 4, 5} if repeats are possible?

Mr. Jones owns 4 pairs of pants, 7 shirts, and 3 sweaters. In how many ways may he choose 2 of the pairs of pants, 3 of the shirts, and 1 of the sweaters to pack for a trip?

Suppose you are asked to list, in order or preference, the three best movies you have seen this year. If you saw 10 movies during the year, in how many ways can the three best be chosen and ranked?

There are 110 people at a meeting. They each shake hands with everyone else. How many handshakes were there?

A group of 45 people are going to run a race. The top three runners earn gold, silver, and bronze medals.

How many different committees of 5 people can be chosen from 10 people?

A team of 8 basketball players needs to choose a captain and co-captain. How many ways are there to do this?

In how many ways may 8 people form a circle for a folk dance?

5. Suppose a True-False test has 20 questions. a) In how many ways may a student mark the test, if each question is answered?

You just bought 3 tickets to the Yankees and you have 5 friends you could invite. How many different combinations of friends could you choose to join you at the game?

Suppose you find 7 articles related to the topic of your research paper. In how many ways can you choose 5 articles to read?

Selecting which seven players will be in the batting order on a 11 person team.

How many permutations are there of the letters in the word “greet”?