tions 7- 10: A doughnut shop sells 30 kinds of doughnuts. In how many ways can y

Question

tions 7- 10: A doughnut shop sells 30 kinds of doughnuts. In how many ways can yo 7. get a bag of 15 doughnuts? a) C(3o,15) b) C(44,29) c) C(15,30) d) C(45,15) e) None of the above 8. ag of 15 doughnuts if you want at least 3 glazed doughnuts and at least 4 raspberry doug a) C(30,7) b) C(15,7) c) C(37,29) d) C(44,29) c) None of the above 9. get a bag of 15 doughnuts if you want exactly 3 glazed doughnuts and exactly 4 raspberry d a) C(15,7) b) C(30,7) c) C(35,15) d) C(35,27) e) None of the above . get a bag of 15 doughnuts if you want at least 3 glazed doughnuts and at most 1 raspberry a) C(39,28)+C(40,28) b) C(44,29) c) C(39,28) d) C(40,28) ) None of the above

Explanation / Answer

7.
There are C(n,r) ways to choose r element from n elements.
Here there are 30 different doughnuts and we want to select 15 out of them.
Hence there are C(30,15) ways to do it.

8.
Here we need to select at least 3 glazed doughnuts and at least 4 raspberry doughnuts.
Hence out of 15, (4+3=7) choices are already made.
so we can say that we need to choose 15-7 = 8 doughnuts out of 30 doughnuts.
number of ways to do it = C(30, 8).
Hence none of these is answer.

9.
If we want exactly 3 glazed doughnuts and exactly 4 raspberry doughnuts then:
We need to choose from 30-2 = 28 doughnuts.

Here we need to choose 8 doughnuts from 28 doughnuts.

Number of ways to do it = C(28,8)

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