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counting and probability senior

Problem

Suppose 5 different integers are randomly chosen from between 20 and 69, inclusive. What is the probability that they each have a different tens digit?
Solution
In this set of integers, there are 5 tens digits: {2, 3, 4, 5, 6}. If 5 integers all have different tens digits, then there must be exactly one integer among the 5 with each tens digit. Since there are 10 different integers for each tens digit, the number of ways to pick, without regard to order, 5 different integers with different tens digits is . The total number of combinations of 5 integers is . So the probability that 5 integers drawn all have the different tens digits is
Final answer
\frac{2500}{52969}