There are 330 different ways for choosing a dozen donuts from the 4 varieties at a donut shop. (at least one donut of every variety must be selected)
<h3>How to calculate the number of ways to select items?</h3>There are 'r' items from 'n' different varieties (repetition allowed). Then, the number of ways to select items is given by
The number of ways =
Where the combination is calculated as
It is given that there are 4 varieties of donuts in a shop. I.e., n = 4
Number of donuts to be selected r = 12 (one dozen)
And also given that at least one donut of every variety has to be selected.
Since there are 4 varieties, at least one from each of these means the count is 4.
So, the remaining number of donuts to be selected is 12 - 4 = 8.
So, r becomes 8 i.e., r = 8
On substituting,
the number of ways of selecting the remaining 8 donuts =
⇒
⇒
⇒
⇒ 330
Therefore, there are 330 different ways for choosing a dozen donuts from the 4 varieties at a donut shop.
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