Let's imagine a die roll. You roll the die n times.
Example: I have a $6$ sided die. Assuming the distribution of the die is perfect, the chances of getting any single number are $1/6$. The chances of getting two consecutive same numbers (by rule of product) are $1/36$. The chances of getting any two specific numbers (let's assume a random pair like $(2,3)$) are $1/36$ also.
Let's assume that pairs of type $(n,m)$ are equivalent to pairs of type $(m,n)$ - we count them as equal. So when we roll the die n times, is the chance of some pair $(m,n)$ appearing greater than the chance of a pair $(n,n)$ appearing? That is to say is the chance of getting $(2,3)$ & $(3,2)$ in a row bigger than just the chance of getting $(4,4)$ & $(4,4)$ in a row?