In a high school math competition, there are 10 distinct problems to solve. Each contestant must solve 5 problems, and the order in which they select these problems matters. How many different combinations of 5 problems can be selected from the 10 available problems?
If a contestant instead could select any 5 problems without regard to the order, how many combinations would there be?
Express your final answer as the total number of combinations of problems if both selecting with order and without order are considered.