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 of doing both.

A permutation is the arrangement of objects in a specific order. The number of permutations of n distinct objects taken r at a time is given by the formula: nPr = n! / (n - r)!

A combination is a selection of objects without considering the order. The number of combinations of n distinct objects taken r at a time is given by the formula: nCr = n! / (r! * (n - r)!)

The sample space is the set of all possible outcomes of an experiment. It is denoted by S.

An event is a subset of the sample space, representing the outcomes of interest.

The probability of an event A, denoted by P(A), is the ratio of the number of favorable outcomes to the total number of possible outcomes.

Use the fundamental counting principle to determine the number of outcomes for a given scenario.

If there are 3 different shirts and 4 different pants, how many different outfits can be created?

Solution: By the fundamental counting principle, the number of different outfits is 3 * 4 = 12.

Use the permutation formula to calculate the number of arrangements of objects.

How many different 3-letter arrangements can be made using the letters A, B, C, and D?

Solution: The number of permutations is 4P3 = 4! / (4 - 3)! = 4 * 3 * 2 = 24.

Use the combination formula to calculate the number of selections of objects.

A committee of 5 members is to be formed from a group of 10 people. How many different committees can be formed?

Solution: The number of combinations is 10C5 = 10! / (5! * (10 - 5)!) = 252.

Calculate the probability of an event using the ratio of favorable outcomes to total outcomes.

What is the probability of rolling a 3 on a fair six-sided die?

Solution: The probability is P(3) = 1/6.

By mastering the fundamental counting principle, permutations, combinations, and theoretical probability, you will have a solid foundation in understanding and calculating probabilities in various scenarios.

.Study GuideTheoretical probability and counting Worksheet/Answer key

Theoretical probability and counting Worksheet/Answer key

Theoretical probability and counting Worksheet/Answer key

Theoretical probability and counting

DATA ANALYSIS, STATISTICS, AND PROBABILITY

Understand that, just as with simple events, the probability of a compound event is the fraction of outcomes in the sample space for which the compound event occurs. Understand and use appropriate terminology to describe independent, dependent, complementary, and mutually exclusive events.

For events with a large number of outcomes, understand the use of the multiplication counting principle. Develop the multiplication counting principle and apply it to situations with a large number of outcomes.