JEE Main 2019 (Online) 9th January Morning ShiftQuestion 1
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:
Permutation and Combination
Solution
Concept. Choose girls freely; for boys remove the teams having both $A$ and $B$. Formulas used. (1) ${}^nC_r=\frac{n!}{r!\,(n-r)!}$Step 1 - Girls. ${}^5C_2=10$. Step 2 - All boy choices. ${}^7C_3=35$. Step 3 - Both A and B. Third boy from the other $5$: ${}^5C_1=5$. Step 4 - Allowed boys. $35-5=30$. Step 5 - Total. $10\cdot30=300$. Answer: A