Counting, Permutations, and Combinations(KA/SAP/U8CountingAndOthers)

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Unit 8: Counting, Permutations, and Combinations

Topics:
  • Counting principle and factorial
  • Permutations
  • Combinations
  • Combinatorics and probability

Counting Principle and Factorial

The counting principle helps us find the total number of possible outcomes by multiplying the number of choices for each event. For example, if you have 3 shirts and 2 pants, you have 3 × 2 = 6 possible outfits.

The factorial of a number n (written as n!) is the product of all positive integers up to n. For example, 4! = 4 × 3 × 2 × 1 = 24.

Quiz: What is 6! ?

Permutations

A permutation is an arrangement of objects in a specific order. The number of ways to arrange n objects is n! If you want to arrange r objects out of n, use the formula: P(n, r) = n! / (n - r)!

Quiz: How many ways can you arrange 4 books on a shelf?

Combinations

A combination is a selection of objects where order does not matter. The number of ways to choose r objects from n is: C(n, r) = n! / (r! × (n - r)!)

Quiz: How many ways can you choose 2 students from a group of 6?

Combinatorics and Probability

Combinatorics helps us count possible outcomes, which is essential for calculating probabilities. The probability of an event is the number of favorable outcomes divided by the total number of possible outcomes.

Quiz: If you flip a coin 3 times, what is the probability of getting exactly 2 heads?

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