An employee of a grocery store is placing an order for soda. There are 8 varieti

Question

An employee of a grocery store is placing an order for soda. There are 8 varieties of soda and they are sold in cases. Each case contains is all the same variety. The store will order 50 cases total.

-How many ways are there to place the order?

-How many ways are there to place the order if she orders at least 3 of each variety?

-How many ways are there to place the order if she does not order more than 20 cases of Coke?

-How many ways are there to place the order if she does not order more than 25 of any single variety?

-How many ways are there to place the order if she does not order more than 20 of any single variety?

Explanation / Answer

It is given that there are 8 varieties of soda and the store will order 50 cases total.
a) Ways to place the order is given by 50P8 = 2.16 x 1013

b) Ways to place the order if she orders at least 3 of each variety = 26P8 = 6.299 x 1010

c) Ways to place the order if she does not order more than 20 cases of Coke = 57P7 - 36P7 = 1.29 x 1012

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