What is the number of selections of at most 3 things from 6 different things?

Step-by-step solution

The number of ways to select r things from n different things is given by ^ n C_ r . The phrase "at most 3 things" means we can select 0, 1, 2, or 3 things from the 6 available different things. The total number of selections is the sum of these possibilities: ⁶C₀ + ⁶C₁ + ⁶C₂ + ⁶C₃ Calculating each term: ⁶C₀ = 1 ⁶C₁ = 6 ⁶C₂ = 6 5 2 1 = 15 ⁶C₃ = 6 5 4 3 2 1 = 20 Total number of selections = 1 + 6 + 15 + 20 = 42 . Answer: 42