NDA Mathematics Question (2025) — Solution

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: ^ 6 C_ 0 + ^ 6 C_ 1 + ^ 6 C_ 2 + ^ 6 C_ 3 Calculating each term: ^ 6 C_ 0 = 1 ^ 6 C_ 1 = 6 ^ 6 C_ 2 = 6 5 2 1 = 15 ^ 6 C_ 3 = 6 5 4 3 2 1 = 20 Total number of selections = 1 + 6 + 15 + 20 = 42. Answer: 42