Home › MCQs › EEJ MAIN Mathematics › Question #6935
Back to Questions
EEJ MAIN Mathematics QUESTION #6935
Question 1

A class has 5 girls and 7 boys. Teams of 2 girls and 3 boys are to be formed. However, two specific boys A and B cannot both be on the same team. How many valid teams can be formed?

  • 500
  • 200
  • 300✔️
  • 350
Correct Answer Explanation

Total teams (no restriction): $\binom{5}{2}\binom{7}{3} = 10 \times 35 = 350$

Teams where both A and B are included: Choose remaining 1 boy from 5 others: $\binom{5}{2}\binom{5}{1} = 10 \times 5 = 50$

Valid teams $= 350 - 50 = \mathbf{300}$