Math CentralQuandaries & Queries


Subject: permutation combination
Name: Mel
Who are you: Student

how many ways can you buy a dozen donuts from an unlimited supply of five types of donuts?

Hi Mel,

One way to look at this is arrangements of 12 O's (donuts) and 4 |'s (dividers between the boxes of donuts) so that, for example OOO||OOOOO|OOO|O means that you buy 3 donuts of the first type, none of the second type, 5 of the third type, 3 of the fourth type, and 1 of the fifth type. So what you need to figure out is how many ways can you arrange 12 O's and 4 |'s in a line. The best way to think of this is in how many ways can you place the 12 O's into the 16 places which is ... .



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