4.7/4.8 Homework - Permutations vs. Combinations

Front

What is a combination?

Back

A way of choosing items from a large set of objects where the order does not matter.

Front

What is a permutation?

Back

A way of arranging items from a set where the order does matter.

Front

When would you use combinations instead of permutations?

Back

When the order of selection does not affect the outcome.

Front

When would you use permutations instead of combinations?

Back

When the order of selection affects the outcome.

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.

Front

Example of a combination problem: Choosing 3 fruits from a basket of 5. How many combinations are there?

Back

C(5, 3) = 10.

Front

Example of a permutation problem: Arranging 4 books on a shelf from a selection of 6. How many arrangements are there?

Back

P(6, 4) = 360.

Front

What is the Multiplication Counting Principle?

Back

If there are m ways to do one thing and n ways to do another, then there are m × n ways to do both.

Front

In the context of PIN codes, why is it a permutation?

Back

Because the order of the digits matters in determining the code.