There are 10 distinct oranges in a basket. In how many ways can 3 oranges be chosen? (Treat oranges as distinct items; order of selection does not matter.)

Introduction / Context:This is an elementary combinations problem: selecting k items from n distinct items without regard to order is counted by C(n, k).

Given Data / Assumptions:

• n = 10 distinct oranges.
• k = 3 oranges chosen.
• Order is irrelevant.

Concept / Approach:Use C(10, 3) = 10! / (3! * 7!).

Step-by-Step Solution:

Verification / Alternative check:Check with symmetry: C(10, 3) = C(10, 7) also equals 120.

Why Other Options Are Wrong:125, 140, and 110 are common miscomputations; 120 is the unique correct combination count.

Common Pitfalls:Using permutations (10P3) instead of combinations, thereby overcounting by 3!.

Final Answer:120