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elixir [45]
1 year ago
8

How many different ways are there to choose a dozen donuts from the 4 varities at a donut shop so that you get atleast one donut

of every variety g
Mathematics
1 answer:
Leno4ka [110]1 year ago
5 0

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 =  _{n+r-1}C_r

Where the combination _{n}C_r is calculated as

_{n}C_r=\frac{n!}{r!(n-r)!}

<h3 /><h3>Calculation:</h3>

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 = _{4+8-1}C_4

⇒ _{11}C_4

⇒ \frac{11!}{4!(11-4)!}

⇒ \frac{11!}{(4!)(7!)}

⇒ 330

Therefore, there are 330 different ways for choosing a dozen donuts from the 4 varieties at a donut shop.

Learn more about combinations here:

brainly.com/question/11732255

#SPJ4

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