Question

In a group of 6 people, 3 are selected for a team. How many ways can the team be formed?

• A. 15
  
• B. 20
  
• C. 25
  
• D. 30
  

Hint:

For team selection, use $\binom{n}{k}$ for combinations without order.

Answer 1

The Correct Option is B

- Step 1: Use combinations. Choose 3 people from 6: $\binom{6}{3}$.
- Step 2: Calculate. $\binom{6}{3} = \frac{6 \times 5 \times 4}{3 \times 2 \times 1} = 20$.
- Step 3: Verify. Alternative: $\binom{6}{3} = \binom{6}{3} = 20$.
- Step 4: Compare with options. Options: (1) 15, (2) 20, (3) 25, (4) 30. Matches 20.
- Step 5: Cross-check. List some teams (A, B, C, D, E, F): ABC, ABD, etc. Total = 20.
- Step 6: Conclusion. Option (2) is correct.