JEE Main 2013 (Online) 9th AprilQuestion 1
A committee of $4$ persons is to be formed from $2$ ladies, $2$ old men and $4$ young men such that it includes at least $1$ lady, at least $1$ old man and at most $2$ young men. Then the total number of ways in which this committee can be formed is :
Permutation and Combination
Solution
Concept. List all $(L,O,Y)$ with $L\ge1$, $O\ge1$, $Y\le2$, sum $4$ (and $L,O\le2$). Formulas used. (1) ${}^nC_r=\frac{n!}{r!\,(n-r)!}$Step 1 - $(1,1,2)$. $2\cdot2\cdot{}^4C_2=24$. Step 2 - $(2,1,1)$. $1\cdot2\cdot4=8$. Step 3 - $(1,2,1)$. $2\cdot1\cdot4=8$. Step 4 - $(2,2,0)$. $1$. Step 5 - Add. $24+8+8+1=41$. Answer: B