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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?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?

Question
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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Step 1

(a) The shop has 7 types of croissants.

So n = 7. To choose one dozen croissants, so r = 12.

Repetition of croissants are allowed.

Thus the number of ways are

(7 12-1
nr1
12
18
(12
18!
12!(18-12
18!
12!6!
18564 ways
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(7 12-1 nr1 12 18 (12 18! 12!(18-12 18! 12!6! 18564 ways

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Step 2

(b) The shop has 7 types of croissants.

So n = 7. To choose two dozen croissants, so r = 24.

Repetition of croissants are allowed.

Thus the number of ways are

(7+24 1
nr-1
24
(30
24
30!
24!(30 24)
30!
24!6!
= 593775 ways
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(7+24 1 nr-1 24 (30 24 30! 24!(30 24) 30! 24!6! = 593775 ways

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Step 3

(c) The shop has 7 types of croissants.

So n = 7.

First select 1 of each kind, which are 7 croissants in total. Still need to select the re...

(7+5-1
n+r-1
5
(11)
5
11!
51(11-5)
11!
5!6!
462 ways
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(7+5-1 n+r-1 5 (11) 5 11! 51(11-5) 11! 5!6! 462 ways

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