Final answer:
There are 252 different paths from the bottom left to the top right of a 5x5 grid when moving only up and right.
Step-by-step explanation:
To find the number of paths from the bottom left to the top right of a 5x5 grid, when moving only up and right, we can use the concept of combinations.
The total number of steps needed to reach the top right corner is 5 steps right and 5 steps up, which is a total of 10 steps.
Using the formula for combinations, we can calculate the number of paths:
C(10, 5) = (10!)/(5!*(10-5)!)
Simplifying this expression, we get: C(10, 5) = 252
Therefore, there are 252 different paths from the bottom left to the top right of a 5x5 grid when moving only up and right.