"How plenty of ways are there to pick a dozen donuts indigenous the 21 varieties at a donut shop?"
I figured the answer would certainly be simple C(21, 12), however it turns out we're enabled to pick any amount of every donut. The prof wrote down the the answer is C(21 + 12 -1; 21 - 1) = C(32; 20) = C(32; 12)
I deserve to barely wrap my head around why it's 21 + 12, ns have also less idea whereby the "-1" comes from, or whereby the 21 come from.
You are watching: How many different ways are there to choose a dozen donuts from the 21 varieties at a donut shop
Every variation I've checked out posted of this inquiry online is a variation where precisely 12 donuts are chosen. Say thanks to you because that reading.
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The 21+12 and also -1 you space confused about are simply from one equation that the professor must have actually failed to explain or friend missed in your notes. Once you have actually 'n' elements and also are walking to pick a collection of 'k' the them through repetition, over there is a formula: (n+k-1;k-1) = (n+k-1;n-1) so in your case, n=21, k=12 and if friend plug those in you will get precisely what her professor said you.
I hope this pushes friend in the best direction.
Op · 9y
Thanks a lot for her help.
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