Consider the path as two movements - from O to C, and then from C to A.
From O to C, there are five movements you need to make, however two of them must be up and three of them must be right. Hence the
.
If you do the same for the movement from C to A, you will see how they get the second fraction.
As you need to move from O to C AND C to A, you therefore multiply the two fractions to get the number of paths.