Gold medalist, in freestyle skiing, Justine Duford-Lapointe, is trying to get to her hotel. She can only 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 total number of possible paths by moving only north and east.
Let's break down the problem into smaller grids to simplify the calculation.
First, let's consider the 5x5 grid. In a 5x5 grid, in order to reach the top-right corner (the hotel), she needs to take four steps north and four steps east. The number of possible ways to do this is calculated using the binomial coefficient, also known as "n choose k," which represents the combination formula (nCk). In this case, we want to calculate 8C4, which is equal to (8!)/(4! * (8-4)!), resulting in 70 possible paths in the 5x5 grid.
Next, we have a 2x2 grid. In a 2x2 grid, she must take one step north and one step east to reach the top-right corner. Thus, there is only one possible path in the 2x2 grid.
Finally, we have an 8x8 grid. In an 8x8 grid, she needs to take eight steps north and eight steps east to reach the top-right corner. Using the same concept as before, the number of possible paths can be calculated as 16C8, which is equal to (16!)/(8! * (16-8)!), resulting in 12,870 possible paths in the 8x8 grid.
To find the total number of ways to reach the hotel, we multiply the number of possible paths in each grid: 70 * 1 * 12,870 = 900,900.
Therefore, there are 900,900 ways for Justine Duford-Lapointe to reach her hotel.