Please explain in great details. Don\'t skip intermediate steps. I am trying to
ID: 3715954 • Letter: P
Question
Please explain in great details. Don't skip intermediate steps. I am trying to really understand this. Thank you.
3. A doughnut shop sells 30 kinds of doughnuts. In how many ways can you (a) get a bag of 12 doughnuts? Answer Your work: [Show how to determine n and r and the formula used. (b) get a bag of 12 doughnuts if you want at least 3 glazed doughnuts and at least 4 raspberry doughnuts? Answer: Your work: [Show how to determine n and r and the formula used.] (e) get a bag of 12 doughnuts if you want exactly 3 glazed doughnuts and exactly 4 raspberry doughnuts? Answer: Your work: [Show how to determine n and r and the formula used.)Explanation / Answer
a)
Total type of donuts (n) = 30
donuts to be selected (r) = 12
No. of ways to selection of 12 donuts = nCr = 30C12 = (30!) / (12! * (30 - 12)!) = (30!) / (12! * (18)!) = 86,493,225
b)
Select 12 Donuts in which atleast 3 are grazed and 4 are rasberry therefore 3+4 = 7 donuts are fixed hence 12-7 = 5 donuts are to be selected among 30 donuts (as atleast 3 are grazed and 4 are rasberry atmost is not define) therefore,
n = 30
r = 5
nCr = 30C5 = (30!) / (5! * (30-5)!) = (30!) / (5! * (25)!) = 142,506
c)
12 donuts are selected among them exactly 3 are gazed and 4 are rassberry therefore 3+4 = 7 donuts are fixed and also the remaining 12-7 = 5 donuts which are to be selected must not be of gazes and resberry type (exactly 3 are gazed and 4 are rassberry ). Hence 5 donuts are selected among 30-2 =28 types of donuts
n = 28
r = 5
nCr = 28C5 = (28!) / (5! * (28-5)!) = (28!) / (5! * (23)!) = 98,280