FCP, Combinations, and Permutations

Front

What is a combination?

Back

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

Front

What is a permutation?

Back

A permutation is an arrangement of items from a larger set where the order does matter.

Front

What is the Fundamental Counting Principle (FCP)?

Back

The Fundamental Counting Principle states that if one event can occur in 'm' ways and a second event can occur independently in 'n' ways, then the two events can occur in m × n ways.

Front

When would you use combinations instead of permutations?

Back

Use combinations when the order of selection does not matter, such as choosing members for a committee.

Front

When would you use permutations instead of combinations?

Back

Use permutations when the order of arrangement matters, such as assigning roles or positions.

Front

How many ways can you choose 3 representatives from a group of 165 students?

Back

This is a combination problem, calculated as C(165, 3).

Front

How many ways can you arrange 3 officers from a ski club of 10 members?

Back

This is a permutation problem, calculated as P(10, 3) = 720.

Front

If you have 14 types of candy bars and want to choose 5, how do you calculate this?

Back

This is a combination problem, calculated as C(14, 5) = 2002.

Front

What is the formula for 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

What is the formula for 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.