Final answer:
There are 252 different ways to select 5 problems from a 10-item mathematics test.
Step-by-step explanation:
In a 10-item mathematics problem solving test, you need to select 5 problems to solve. To determine the number of ways to do this, we can calculate the number of combinations using the formula 10 choose 5. This can be expressed as 10C5, which is equal to 10!/(5!(10-5)!).
Simplifying this expression, we get 10!/(5!5!) = (10*9*8*7*6)/(5*4*3*2*1) = 252.
Therefore, there are 252 different ways to select 5 problems from a 10-item mathematics test.