Question

Consider a class of 5 girls and 7 boys. The number of different teams consisting of 2 girls and 3 boys that can be formed from this class, if there are two specific boys A and B, who refuse to be a member of same team, is :

• A. 200
• B. 300
• C. 350
• D. 500

Answer 1

The correct option is B 300

Given :
Number of girls = 5 ; number of boys = 7.
Team consist of 2 girls and 3 boys.
Number of teams which do not have A and B together
= total number of teams possible - number of teams with A and B together

Total number of teams$=5_{C_2}\times 7_{C_3}=10\times 35=350$
Number of teams with A and B together $=5_{C_2}\times 5_{C_1}=10\times 5=50$
Hence, possible number of teams which do not have A and B together $=350-50=300$