Question

Let the range of the function $f :\{1,2,3,4,5\} \rightarrow\{1,2,3,4,5\}$ assumes exactly 3 distinct values. If the number of such function is $N$, then find the value of $\frac{ N }{300}$.

Answer 1

Since range contains exactly 3 distinct values

$\therefore { }^5 C _3\left[\frac{5 !}{1 ! 1 ! 3 !} \frac{1}{2 !}+\frac{5 !}{1 ! 2 ! 2 !} \frac{1}{2 !}\right] \times 3 !=1500 .$
So, $ \frac{ N }{300}=\frac{1500}{300}=5$.