Permutations, Combinations, & Set Theory

Front

What is a permutation?

Back

A permutation is an arrangement of objects in a specific order. The number of permutations of n objects taken r at a time is denoted as nPr.

Front

What is a combination?

Back

A combination is a selection of objects without regard to the order. The number of combinations of n objects taken r at a time is denoted as nCr.

Front

What does _nP_r represent?

Back

It represents the number of ways to arrange r objects selected from n distinct objects.

Front

What does _nC_r represent?

Back

It represents the number of ways to choose r objects from n distinct objects without regard to the order.

Front

How do you calculate permutations?

Back

The formula for permutations is nPr = n! / (n - r)!, where n is the total number of objects and r is the number of objects to arrange.

Front

How do you calculate combinations?

Back

The formula for combinations is nCr = n! / (r! * (n - r)!), where n is the total number of objects and r is the number of objects to choose.

Front

What is the difference between permutations and combinations?

Back

Permutations consider the order of selection, while combinations do not.

Front

If A = {1, 2, 3} and B = {2, 3, 4}, what is A ∩ B?

Back

A ∩ B = {2, 3}, which represents the intersection of sets A and B.

Front

If A = {1, 2, 3} and B = {2, 3, 4}, what is A ∪ B?

Back

A ∪ B = {1, 2, 3, 4}, which represents the union of sets A and B.

Front

What is the formula for the number of subsets of a set?

Back

The number of subsets of a set with n elements is 2^n.