The solution is there but I could not understand it. There is another person on chegg that got the answer c=1, which is different from the answer here. I am confused.

9. Let X be a discrete random variable with the following probability mass function p(x)=cx!xe,x=1,2,3, where >0. Find the constant c such that p is a probability mass function. Solution. Note that x=1p(x)=cx=1x!xe=1 and e+x=1x!xe=1. Hence, c=1e1