In how many ways can you make Rhe border if it requires 15 titles and you use only blue and white ones? Explain your reasoning.
The final answer is 8008.
To determine the number of ways you can create a border using 15 tiles, with only blue and white tiles, you can use combinations combining permutations.
First, let's consider the number of blue tiles in the border. It can be any number from 0 to 15, inclusive.
For each number of blue tiles, the remaining tiles will be filled with white tiles. So, the number of white tiles will be the total number of tiles (15) minus the number of blue tiles.
Now, for each number of blue tiles, we will calculate the number of ways to arrange these tiles. This can be done using the formula for combinations, which is given by:
C(n, k) = n! / (k! * (n - k)!)
Where n is the total number of tiles (15), and k is the number of blue tiles.
Using this formula, we can determine the number of arrangements for each value of k.
Finally, we sum up all the arrangements for each possible value of k, from 0 to 15, to get the total number of ways to create the border:
Total number of ways = C(15, 0) + C(15, 1) + C(15, 2) + ... + C(15, 15)
Calculating this expression will give us the final answer, which is 8008.
To verify this, you can use a calculator or a programming language that supports combinations and permutations to calculate each term in the sum and then add them up.