how many rectangles are there on a chess board

so if you have this 8x4 right here we're going to find out how many rectangles do we have right here i'll give you guys five seconds right for you to one i know we did this before already but i will show you guys how to do this in like 15 seconds so here's the deal look at this for rectangle of course we have time and bottom right so as you can see we have a total of one two three four nine lines right here so all we have to do is just choose two lines right so let's say we can choose right here and maybe right here and as we can see the number of ways to do so it's just gonna be nine choose two and then we have to choose the size right so let's say we choose the size right here and then again let's say right here and as you can see we get our rectangles here so all together we have to multiply by another 9 choose 2. and i choose 2 right here it's just going to be 9 times 8 divided by 2 times 1 and of course this is the same thing right here and this is just going to be 36 times 36 so we have 12 1296 and then we are done

Channel: FAST!

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Keywords: how many rectangles are there on a chess board

Id: D9ruTvPEAOk

Length: 0min 52sec (52 seconds)

Published: Fri Sep 10 2021