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

Using the binomial coefficient formula, the number of different paths is 286.

Step-by-step explanation:

To find the number of different paths in a 3×10 grid, we can use combinatorics.

The total number of steps needed to reach the upper right corner is 3+10=13, as we need to make 3 steps up and 10 steps to the right.

Since we need to choose which 10 out of the 13 steps are the steps to the right, we can use the binomial coefficient formula to calculate the number of different paths:

C(13, 10) = 13! / (10! * (13-10)!)

= 286.

Therefore, there are 286 different paths possible.

Answer 2

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)=
`(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)=
`(13!)/(10!(13-10)!) =286`

286 paths are possible!