From (5) red balls and (3) black balls, how many ways are there to choose (2) red balls?

Correct answer: 10

The selection is made only from the 5 red balls, so the number of black balls is irrelevant. Therefore, the number of ways is \(\binom{5}{2}=\frac{5\times4}{2\times1}=10\). Option 15 equals \(\binom{6}{2}\), so it does not apply to 5 red balls. Exam tip: Use \(\binom{n}{r}\) when the order of selection does not matter.