Section 9.2: Permutations & Combinations

This section covers counting methods, including permutations (ordered arrangements) and combinations (unordered selections). Learn how to calculate the number of possible outcomes.

Example 1: Permutations

How many ways can 3 books be arranged on a shelf from a collection of 5?

Step 1: Use permutation formula: \( P(n, r) = \frac{n!}{(n-r)!} \)

Step 2: \( P(5,3) = 5! / (5-3)! = 5*4*3 = 60 \)

Answer: 60 arrangements

Example 2: Combinations

From 8 students, how many ways can a committee of 3 be selected?

Step 1: Use combination formula: \( C(n,r) = \frac{n!}{r!(n-r)!} \)

Step 2: \( C(8,3) = 8! / (3! * 5!) = 56 \)

Answer: 56 ways

Practice Problems

  1. Arrange 4 different trophies on a shelf. How many ways?
  2. Choose 2 students from a group of 6 for a prize. How many combinations?
  3. Arrange 5 letters from the word “ALGER” in order. Number of arrangements?
  4. Select 3 cards from a deck of 52. Number of combinations?
  5. From 10 runners, pick 1st, 2nd, 3rd place winners. How many ways?
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