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 given by n! / (n - r)!.

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 given by n! / (r! * (n - r)!).

Front

Calculate 20P2.

Back

20P2 = 20! / (20 - 2)! = 20! / 18! = 20 × 19 = 380.

Front

What is the intersection of two sets A and B?

Back

The intersection of two sets A and B, denoted A ⋂ B, is the set of elements that are common to both A and B.

Front

If A = {1, 2, 3, 4, 5, 6} and B = {1, 2, 3, 5, 7, 9}, what is A ⋂ B?

Back

A ⋂ B = {1, 2, 3, 5}.

Front

How many ways can a coach choose 5 starting players from 11 players?

Back

The number of ways to choose 5 players from 11 is given by 11C5 = 462.

Front

What is the formula for combinations?

Back

The formula for combinations is 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 does the symbol '∪' represent in set theory?

Back

The symbol '∪' represents the union of two sets, which is the set of elements that are in either set A, set B, or both.

Front

What does the symbol '∩' represent in set theory?

Back

The symbol '∩' represents the intersection of two sets, which is the set of elements that are common to both sets.

Front

What is the complement of a set A?

Back

The complement of a set A, denoted A', is the set of all elements not in A.