Combinatorics

Front

What is Combinatorics?

Back

Combinatorics is a branch of mathematics dealing with combinations, arrangements, and counting of objects.

Front

Define 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

Define 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

What is a Factorial?

Back

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

Front

What is a Tree Diagram?

Back

A tree diagram is a visual representation used to show all possible outcomes of a situation, often used in probability and combinatorics.

Front

How many different models of a car can you buy if there are 9 colors, 3 styles, and 2 sizes?

Back

54 different models (9 colors × 3 styles × 2 sizes = 54).

Front

How many ways can you select 4 cards of the same suit from a deck?

Back

2,860 ways.

Front

If a book club offers a choice of 8 books from a list of 40, how many ways can a member make a collection?

Back

The number of ways is given by the combination formula: C(40, 8).

Front

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

Back

504 ways (9P3 = 9! / (9-3)! = 504).

Front

In how many ways can 4 letters be chosen from the word RANDOMLY?

Back

70 ways.