Question

In how many ways can a committee of 3 be chosen from 6 people?

• A. 15
• B. 20
• C. 30
• D. 60

Hint:

Use $\binom{n}{r}$ for choosing items where order doesn't matter.

Answer 1

The Correct Option is B

- Step 1: Combinations formula. $\binom{n}{r} = \frac{n!}{r!(n-r)!}$. For $n = 6$, $r = 3$:
\[ \binom{6}{3} = \frac{6 \cdot 5 \cdot 4}{3 \cdot 2 \cdot 1} = 20. \] - Step 2: Verify. List some: $\binom{6}{3} = 20$ is standard.
- Step 3: Conclusion. Option (2) 20 is correct.