Fundamental Counting Principle

Front

What is the Fundamental Counting Principle?

Back

The Fundamental Counting Principle states that if one event can occur in 'm' ways and a second event can occur independently in 'n' ways, then the total number of ways both events can occur is m × n.

Front

How many different 1-scoop ice cream cones can a customer order if there are 3 types of cones and 31 flavors of ice cream?

Back

93 (3 cones × 31 flavors = 93 combinations).

Front

How many different ways can Brianna arrange her schedule of 6 classes?

Back

720 (6! = 6 × 5 × 4 × 3 × 2 × 1 = 720).

Front

If shoppers are categorized as male or female, over 40 or under 40, and cash or credit card shoppers, how many ways can they be categorized?

Back

8 (2 genders × 2 age groups × 2 payment methods = 8 combinations).

Front

What does a tree diagram represent in counting problems?

Back

A tree diagram visually represents all possible outcomes of a sequence of events, showing how choices branch out.

Front

If there are 3 shirt options, 2 pants options, and 2 shoe options, how many outfit combinations can be made?

Back

12 (3 shirts × 2 pants × 2 shoes = 12 combinations).

Front

What is the total number of outcomes for picking a cat or dog and choosing the colors black, brown, or spotted?

Back

6 (2 animals × 3 colors = 6 combinations).

Front

Define permutations in the context of counting principles.

Back

Permutations refer to the arrangement of objects in a specific order, where the order matters.

Front

Define combinations in the context of counting principles.

Back

Combinations refer to the selection of objects where the order does not matter.

Front

What is the formula for calculating permutations of 'n' items taken 'r' at a time?

Back

P(n, r) = n! / (n - r)!.