I have the following problem for a math competition I am studying for:
25 pebbles are placed in a 5 by 5 grid. How many ways can 5 pebbles be picked so that no two of them are in the same row or column?
The answer key says that the answer is 120 however, I don't know how it got it. I am guessing this has something to do with permutations and/or combinations.
They intend you to choose five pebbles. You have five choices for the pebble in the first row, then four for the one in the second row, and so on to just one in the fifth row. That gives $5!=120$ possibilities.