Name all the arrays you can make with 8 tiles
To find all the possible arrays that can be made with 8 tiles, we need to consider the different combinations and arrangements. An array can be represented as a sequence of tiles placed in a specific order.
To simplify the problem, let's assume that we have 8 distinct tiles labeled from 1 to 8. We can use these tiles to form various arrays. Here are all the possible ways to arrange these tiles:
1. Single tile arrays: There are 8 different single tile arrays, each consisting of only one tile. These arrays can be represented as {1}, {2}, {3}, {4}, {5}, {6}, {7}, {8}.
2. Two tile arrays: There are 28 different two tile arrays, where two tiles are arranged in different orders. These arrays can be represented as {1, 2}, {1, 3}, {1, 4}, ..., {7, 8}.
3. Three tile arrays: There are 56 different three tile arrays, where the three tiles are arranged in different orders. These arrays can be represented as {1, 2, 3}, {1, 2, 4}, {1, 2, 5}, ..., {6, 7, 8}.
4. Four tile arrays: There are 70 different four tile arrays, where the four tiles are arranged in different orders. These arrays can be represented as {1, 2, 3, 4}, {1, 2, 3, 5}, {1, 2, 3, 6}, ..., {5, 6, 7, 8}.
5. And so on, we can continue this process to find arrays with more tiles.
By using combinatorics, we can calculate the total number of arrays that can be formed with 8 tiles. The formula to find the total number of arrays is given by nCr, where n represents the total number of tiles (8 in this case) and r represents the number of tiles in each array. For example, if we want to find the number of arrays with 3 tiles, we calculate 8C3, which equals 8! / (3! * (8-3)!), resulting in 56 arrays.
In summary, the total number of arrays that can be made with 8 tiles is the sum of the combinations at each level, starting from single tile arrays up to all 8 tiles combined.