Let $A = \{1,2,3,4\}$ and $B = \{a,b,c,d,e\}$. How many functions from $A$ to $B$ are either one-to-one or map the element $1$ to $c$? (you need not simplify your answer)
First. the number of functions which are one-to-one : $5\cdot4\cdot3\cdot2$
Second. the number of functions that map the $1$ to $c$ : $5^3$
answer : $5\cdot4\cdot3\cdot2 + 5^3$
is it right? please help me..