Consider a class of 5 girls and 7 boys.

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 the members of the same team, is:

  1. 200

  2. 300

  3. 500

  4. 350


Correct Option: , 2

Solution:

Required number of ways

$=$ Total number of ways $-$ When $\mathrm{A}$ and $\mathrm{B}$ are always included.

$={ }^{5} \mathrm{C}_{2} \cdot{ }^{7} \mathrm{C}_{3}-{ }^{5} \mathrm{C}_{1}^{5} \mathrm{C}_{2}=300$

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