Question

Consider a 3×10 grid of points. Suppose that starting at the lower left corner, you can go one step up or one step to the right at each time. You continue moving until you reach the upper right corner. How many different paths are possible.

Answer 1

Answer:

Step-by-step explanation:

Before to get started we are going to imagine a grid with 3 rows and ten columns.

In order to find how many different paths are possible to reach the upper right corner from the lower left corner  we have to take in account that every possible route has just 13 moves. 3 right moves and 10 up moves.  

Since order does not matter in our paths , we can solve this problem using combination formula.

C(n,r)=$\frac{n!}{r!*(n-r)!}$

Let n=all possible  moves

   r= number of right or up moves

The number of possible paths can be found by finding how many combinations of right moves or up moves we can have in all possible moves. We will end up with he exact same result.  

In this case we will use r as the number of up moves.

C(13,10)=$\frac{13!}{10!(13-10)!} =286$

286 paths are possible!