Fundamental Counting Principle

Front

What is the Fundamental Counting Principle?

Back

The Fundamental Counting Principle states that if there are 'm' ways to do one thing and 'n' ways to do another, then there are m × n ways to do both.

Front

How many outcomes are there for picking a day of the week and a month of the year?

Back

There are 7 days in a week and 12 months in a year. Total outcomes = 7 × 12 = 84.

Front

If you have 5 pairs of jeans, 8 t-shirts, and 2 pairs of shoes, how many outfits can you create?

Back

Total outfits = 5 × 8 × 2 = 80.

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 many choices are available at each step.

Front

How many different versions of a car model can be created with 4 trim levels, 5 colors, and 3 interiors?

Back

Total versions = 4 × 5 × 3 = 60.

Front

At a pizza place, if there are 8 meats, 4 cheeses, 3 crust types, and 2 sauces, how many different pizzas can you create?

Back

Total pizzas = 8 × 4 × 3 × 2 = 192.

Front

What is a combination in counting principles?

Back

A combination is a selection of items where the order does not matter.

Front

What is a permutation in counting principles?

Back

A permutation is an arrangement of items where the order does matter.

Front

How do you calculate the total number of outcomes for multiple independent events?

Back

Multiply the number of outcomes for each independent event.

Front

What is the formula for calculating combinations?

Back

The formula for combinations is C(n, r) = n! / (r!(n-r)!), where n is the total items, and r is the items chosen.