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 outfits can be made with 5 pairs of jeans, 8 t-shirts, and 2 pairs of shoes?

Back

80 outfits (5 × 8 × 2 = 80).

Front

If you roll two dice, how many possible outcomes are there?

Back

36 possible outcomes (6 sides on the first die × 6 sides on the second die = 36).

Front

How many choices does a customer have if an ice cream shop offers 3 types of cones and 31 flavors of ice cream?

Back

93 choices (3 types of cones × 31 flavors = 93).

Front

What is the probability of choosing the letter 'm' from the word MATH and then getting tails when flipping a coin?

Back

1/8 (1/4 chance for 'm' and 1/2 for tails, so 1/4 × 1/2 = 1/8).

Front

If you roll a die and then flip a coin, how many possible outcomes are there?

Back

12 possible outcomes (6 outcomes from the die × 2 outcomes from the coin = 12).

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 events?

Back

Multiply the number of outcomes for each event together.

Front

What is the formula for calculating combinations?

Back

C(n, r) = n! / (r!(n - r)!), where n is the total items, r is the items chosen.