Ok, I have a couple of problems here, and I think I'm getting them right, but maybe someone could push me in a different direction as I'm not 100% sure on them either.
1) 12 people join hands for a circle dance. In how many ways can they do this? I said 12!
How many ways can they join hands if gender matters. I Said 12!/2! , 12 positions and 2 genders.
2) The integers 1-25 are arranged in a 5x5 array from 1-25 exactly once. All that matters is which numbers are in in each column and how they are arranged in the columns. I said 25!/5! , 25 numbers and 5 columns.
3) Two different coins are placed on squares of a standard 8x8 chess board. They can be on the same square. Let us call two arrangements of the coins on the board equivalent if we can move the coins diagonally to get from one arrangement to the other. How many different ways can the coins be placed on the chess board. - This one I have no idea about, I would assume it would be 64!/8! but I'm sort of taking a guess there.
Help is much appreciated!
1) 12 people join hands for a circle dance. In how many ways can they do this? I said 12!
How many ways can they join hands if gender matters. I Said 12!/2! , 12 positions and 2 genders.
2) The integers 1-25 are arranged in a 5x5 array from 1-25 exactly once. All that matters is which numbers are in in each column and how they are arranged in the columns. I said 25!/5! , 25 numbers and 5 columns.
3) Two different coins are placed on squares of a standard 8x8 chess board. They can be on the same square. Let us call two arrangements of the coins on the board equivalent if we can move the coins diagonally to get from one arrangement to the other. How many different ways can the coins be placed on the chess board. - This one I have no idea about, I would assume it would be 64!/8! but I'm sort of taking a guess there.
Help is much appreciated!