JEE Main 2023 (Online) 8th April Evening ShiftQuestion 1
Let $R=\{a,b,c,d,e\}$ and $S=\{1,2,3,4\}$. Total number of onto functions $f:R\to S$ such that $f(a)\neq1$, is equal to $\_\_\_\_\_\_$ .
Functions
Answer$180$
Solution
Onto functions $5\to4$: $4!\,S(5,4)=240$. Those with $f(a)=1$: by symmetry $\frac14$ of them, $60$. So $240-60=180$.