Azhar wants to choose 3 pants out of 5 pants of his collection. How many ways…

Concept: When we need to select r items out of n distinct items and the order of selection does not matter, the number of ways is given by the combination formula: C(n, r) = n! / (r! × (n − r)!).

Application:

1. Here, the total number of pants is n = 5, and Azhar wants to choose r = 3 of them.

2. Number of ways = C(5, 3) = 5! / (3! × 2!)

3. Expanding the factorials: 5! / (3! × 2!) = (5 × 4 × 3 × 2 × 1) / [(3 × 2 × 1) × (2 × 1)]

4. The 3! in the numerator and denominator cancel, leaving (5 × 4) / (2 × 1) = 20 / 2

5. 20 / 2 = 10

Cross-check: Choosing 3 pants to take is equivalent to choosing 2 pants to leave behind, i.e., C(5, 2) = (5 × 4) / (2 × 1) = 10 — the same result, confirming the count.

So there are 10 possible ways to select 3 pants out of 5.