Gold medalist, in freestyle skiing, Justine Duford-Lapointe, is trying to get to her hotel. She can travel north and east. The grid is a 5*5 followed by a 2*2, followed by a 8*8. How many ways can she take to her hotel?
To calculate the number of ways Justine Duford-Lapointe can travel to her hotel, we need to determine the possible paths she can take on the given grid.
Since she can only travel in the north and east directions, she needs to move only in those two directions to reach her destination.
The grid is divided into three parts: a 5x5 grid, a 2x2 grid, and an 8x8 grid. We can calculate the number of paths separately for each part and then multiply these numbers to find the total number of ways.
For the 5x5 grid, Justine needs to move 4 steps to the north and 4 steps to the east to reach the corresponding edges. To calculate the number of ways, we can apply the concept of combinations. We need to choose 4 steps out of the total 8 steps (4 north and 4 east), which can be represented as C(8, 4). Using the formula for combinations, C(n, r) = n! / (r! * (n-r)!), we can calculate C(8, 4) as:
C(8, 4) = 8! / (4! * (8-4)!) = 70
Therefore, there are 70 different ways to move within the 5x5 grid.
Similarly, for the 2x2 grid, Justine needs to move 1 step to the north and 1 step to the east. So, the number of ways to navigate within the 2x2 grid is C(2, 1) = 2.
For the 8x8 grid, Justine needs to move 7 steps to the north and 7 steps to the east to reach her destination. Again, the number of ways to move within this grid is C(14, 7) = 1716.
To find the total number of ways, we multiply the number of ways for each individual grid:
Total number of ways = Number of ways in 5x5 grid * Number of ways in 2x2 grid * Number of ways in 8x8 grid
= 70 * 2 * 1716
= 240,960
Therefore, there are 240,960 different ways for Justine Duford-Lapointe to reach her hotel.