# counting question

• Oct 8th 2009, 12:42 PM
absvalue
counting question
Quote:

The integers 1-25 are arranged in a 5x5 array (we use each number from 1 to 25 exactly once). All that matters is which numbers are in each column, and how they are arranged in the columns. It does not matter in which order the columns appear. How many different such arrays can be formed?
I thought that the answer was $5!^5$, but was told this was wrong. Could someone step me through how to do this?

Thanks!
• Oct 8th 2009, 12:55 PM
Plato
Quote:

Originally Posted by absvalue
The integers 1-25 are arranged in a 5x5 array (we use each number from 1 to 25 exactly once). All that matters is which numbers are in each column, and how they are arranged in the columns. It does not matter in which order the columns appear. How many different such arrays can be formed?

Surely the answer is $(25)!$.
That is the number of ways to arrange the 25 numbers is queue.
Put the first five in the first column, the next five in the second column, etc.
• Oct 8th 2009, 04:30 PM
absvalue
Thanks. :) That makes sense.