JEE Main 2024 (Online) 30th January Evening ShiftQuestion 1
In an examination of Mathematics paper, there are $20$ questions of equal marks and the question paper is divided into three sections: $A,B$ and $C$. A student is required to attempt total $15$ questions taking at least $4$ questions from each section. If section $A$ has $8$ questions, section $B$ has $6$ questions and section $C$ has $6$ questions, then the total number of ways a student can select $15$ questions is $\_\_\_\_\_\_$ .
Permutation and Combination
Answer$11376$
Solution
Valid $(a,b,c)$ with sum 15, $4\le a\le8$, $4\le b,c\le6$: $(5,5,5)$: $56\cdot6\cdot6=2016$; $(4,5,6),(4,6,5)$: $2\cdot70\cdot6=840$; $(5,4,6),(5,6,4)$: $2\cdot56\cdot15=1680$; $(6,4,5),(6,5,4)$: $2\cdot28\cdot15\cdot6=5040$; $(7,4,4)$: $8\cdot15\cdot15=1800$. Total $=11376$.