Two distinct positive integers from 1 to 50 inclusive are chosen. Let the sum of the integers equal $S$ and the product equal $P$. What is the probability that $P+S$ is one less than a multiple of 5?
Here's my logic. We know that $xy+x+y=(x+1)(y+1)-1$. If we need $(x+1)(y+1)-1$ to be $1$ less than a multiple of $5$, we know that $x$ and / or $y$ need to be $1$ less than a multiple of $5$. This means that we have $10*49$ divided by $50*49$. This means our probability is $\frac{1}{5}$. Can someone verify this? Help is greatly appreciated.