11.1 Counting Techniques

Front

What is a combination?

Back

A selection of items from a larger set where the order does not matter.

Front

What is a permutation?

Back

An arrangement of items from a larger set where the order does matter.

Front

How do you calculate combinations?

Back

C(n, r) = n! / (r!(n - r)!) where n is the total number of items and r is the number of items to choose.

Front

How do you calculate permutations?

Back

P(n, r) = n! / (n - r)! where n is the total number of items and r is the number of items to arrange.

Front

What is the fundamental counting principle?

Back

If one event can occur in m ways and a second can occur independently in n ways, then the two events can occur in m × n ways.

Front

If a team of 17 volleyball players needs to choose 3 players, how many different ways can they be chosen?

Back

680

Front

What is the total number of outcomes when tossing a coin and a number cube (1-6)?

Back

12

Front

What does 7P2 represent?

Back

The number of ways to arrange 2 items from a set of 7, which equals 42.

Front

How many different pizzas can you create with 8 meats, 4 cheeses, 3 crust types, and 2 sauces?

Back

192

Front

What is the difference between a permutation and a combination?

Back

A permutation considers the order of selection, while a combination does not.