Permutations, Combinations. & Venn Diagrams CHECK

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

How do you calculate the number of ways to choose r objects from n objects?

Back

Use the formula: C(n, r) = n! / (r! * (n - r)!), where C(n, r) is the number of combinations.

Front

What is the factorial of a number?

Back

The factorial of a number n (denoted as n!) is the product of all positive integers up to n. For example, 5! = 5 × 4 × 3 × 2 × 1 = 120.

Front

How many ways can 4 students be chosen from a class of 15?

Back

Using combinations: C(15, 4) = 15! / (4! * (15 - 4)!) = 1365.

Front

What is a Venn diagram?

Back

A Venn diagram is a visual representation of the relationships between different sets, showing how they overlap.

Front

How do you find the number of elements in the union of two sets?

Back

Use the formula: |A ∪ B| = |A| + |B| - |A ∩ B|, where |A| and |B| are the number of elements in sets A and B, respectively.

Front

If there are 8 violinists, how many ways can they be seated?

Back

The number of ways to seat 8 violinists is 8! = 40320.

Front

What is the difference between permutations and combinations?

Back

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

Front

How many ways can a DJ choose and arrange 3 songs from 9?

Back

Using permutations: P(9, 3) = 9! / (9 - 3)! = 504.