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Combinations

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249
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+275

A set of 25 square blocks is arranged into a 5x5 square. How many different combinations of 3 blocks can be selected from that set so that no two are in the same row or column?

I don't understand the question fully and have no idea on how to approach it.

Aug 15, 2022

#1
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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 25×16×9=3600.

I assume that the question states that the order doesn't matter, so then each collection of three blocks may be chosen in any of six different orders, which leaves the final answer as 3600/3! = 600

If order does matter the answer would be 3600 instead since no overcounting has been done.

Aug 15, 2022
#2
+275
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As stated in the question,  "How many different combinations of 3 blocks can be selected from that set so that no two are in the same row or column?"

Order does matter

Aug 15, 2022