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 the members of the same team, is:

Step-by-step solution

7 B 5 G → 3 B 2 G Total number of ways of forming a team of 3 boys and 2 girls = 7 C 3 × 5 C 2 = 7.6 . 5 1.2 . 3 × 5.4 1.2 = 350 Total number of ways of forming a team if two specific boys B 1 , B 2 always join the team = 5 C 1 × 5 C 2 = 50 So, the total number of ways of forming a team so that two specific boys never come together = 350 - 50 = 300