6. A croissant shop has 7 types of croissants: plain, cherry, chocolate, almond, apple,cheese and hazelnut croissants. How many ways are there to choose:a)dozen croissants?oneb) two dozen croissants?c)one dozen croissants with at least one of each kind?d)one dozen croissants with 2 plain, 1 cherry and at least 2 chocolate?

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Asked Jul 8, 2019
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6. A croissant shop has 7 types of croissants: plain, cherry, chocolate, almond, apple,
cheese and hazelnut croissants. How many ways are there to choose:
a)
dozen croissants?
one
b) two dozen croissants?
c)
one dozen croissants with at least one of each kind?
d)
one dozen croissants with 2 plain, 1 cherry and at least 2 chocolate?
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6. A croissant shop has 7 types of croissants: plain, cherry, chocolate, almond, apple, cheese and hazelnut croissants. How many ways are there to choose: a) dozen croissants? one b) two dozen croissants? c) one dozen croissants with at least one of each kind? d) one dozen croissants with 2 plain, 1 cherry and at least 2 chocolate?

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Expert Answer

Step 1

There are 7 types of croissants.

 

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(a) When there are r-permutations to be made from the collection of objects of k types rk-1 r k- each with an infinite repetition. It is obtained as

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Step 2

Here, a dozen of croissants are chosen, that is r becomes 12 and k becomes 7 as 7 types are there.

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12+7 -1 127 -1 12 7 1 Thus, by formula 18 18 Therefore, to choose a dozen of croissants the number of ways is 6

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Step 3

(b)

Here, a 2-dozen of croissants are chosen, that is r becomes 2...

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24 7-1 24 7-1 24 7-1 Thus, by formula (30 6 30 Therefore, to choose two dozens of croissants the number of ways is 6 Il

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