I was looking at the following question, which asked about the probability that you pick two numbers between $1$ and $10$ without replacement such that they differ by two or more. The accepted answer says
Pick two numbers from $1,2,\ldots,9$ and increase the largest number by one. The resulting pair of numbers will always differ by at least 2 and be numbers in the range $1,\ldots,10$.
This gives a bijection between the problem of choosing two numbers of the 9 and the problem of choosing two numbers of the 10 such that they differ by at least 2. It is important that it is a bijection, i.e. two (or more) pairs of the 9 can't map to the same pair of the 10 that differ by at least two and every pair of the 10 that differ by at least 2 gets mapped to by some pair of the 9. In this case it is trivial to see that $(a,b) \mapsto (a,b+1)$ is indeed a bijection.
but I fail to see how there being a bijection between the two helps you reach the answer of