Question

In how many ways can a committee of 3 people be selected from a group of 7?

• A. 21
• B. 35
• C. 70
• D. 210

Hint:

Order does not matter here. Use the combination formula \( \binom{n}{r} \) with n = 7 and r = 3.

Answer 1

The Correct Option is B

Step 1: A committee has no order, so we count combinations, not permutations. The number of ways to choose 3 from 7 is \( \binom{7}{3} \).

Step 2: Apply the formula \( \binom{n}{r} = \dfrac{n!}{r!\,(n-r)!} \).

\[ \binom{7}{3} = \frac{7!}{3!\,4!} = \frac{7 \times 6 \times 5}{3 \times 2 \times 1} = \frac{210}{6} = 35 \]

Step 3: So there are 35 possible committees. The answer is 35, option (B).