Selection of 3 square blocks from 25 square blocks

Question

A set of $25$ square blocks are arranged into a $5\times5$ square. How many different combinations of $3$ blocks can be selected from the set so that no two are in same row or column?

My try:-

There are $25$ ways to choose the first square.To select second square there are $16$ ways. To select the third square there are $9$ ways.

So, number of ways to choose $3$ square blocks is $25\times16\times9=3600$.

But I am not confident about my answer. Is my answer correct?

It depends whether the order matters or not. You can select the same three blocks in a number of different ways. — Mark Bennet, Nov 01 '17 at 10:10

score 3 · Accepted Answer · answered Nov 01 '17 at 10:11

Whether this answer is correct depends. Do we only care about which blocks are chosen, or do we also care about the order in which they were chosen?

If we care about the order (e.g. picking the top-left, then the middle, then the bottom right block is seen as different from picking the bottom-right, then the top-left, then the middle), then you're good, that's the correct answer.

If the order doesn't matter, then each collection of three blocks may be chosen in any of six different orders, and your method counts each of those six as different. Therefore the answer you have is six times larger than the true answer, and it should really be $600$.

Selection of 3 square blocks from 25 square blocks

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