For a slot machine with 5 reels where there are repeated elements on each of the reel.
Example:
Reel 1 [ 1, 1, 2, 1, 3, 5, 6 ]
Reel 2 [ 1, 2, 3, 4, 5, 5 ]
Reel 3 [ 2, 2, 3, 2, 4 ]
Reel 4 [ 1, 2, 3, 4, 5 ]
Reel 5 [ 1, 2, 3, 4, 5 ]
Are all possibilities (7 x 6 x 5 x 5 x 5) called permutations?
Given, that only one element comes from each of the reels to make a combination. In normal mathematics, is 1-4-2-5-5 the same permutation as 1-4-2-5-5 IF the only difference is the first 1 are on different positions on the first reel?
Please note that a different 1 could effect the other "paylines" such as a diagonal payline vs the main horizontal one. Personally, I believe they are different. I just want to verify my assumptions.
"Pay lines are lines on which the right combination of icons has to appear for a player to win rewards. A pay line can be defined as the line that runs through the reels, intersecting with a symbol on each reel. Different games have different numbers of pay lines – when a particular slots game is described, one of the first things mentioned is how many pay lines it has. Pay lines can vary in number from one onwards – most have less than ten, some less than fifty, and a few less than hundred. Early slot machines all had horizontal pay lines but modern slot games can have pay lines that are zig-zag or diagonal as well as horizontal. Some games even have combinations of different types of pay lines, such as those with three horizontal pay lines and two diagonal ones. The number of pay lines in a particular slot machine game is related to the number of coins that are accepted."
Best Answer
Since each 1 is distinct on the first reel, you should probably label them 1a, 1b,1c. Once you label everything distinctly, it is easier to see that you are correct.
It is confusing to say 1-4-2-5-5 is different than 1-4-2-5-5.
It is clear that 1a-4-2-5-5 is different than 1b-4-2-5-5