Discrete math 1. A doughnut shop sell 30 kinds doughnut. In how many ways can yo

Question

Discrete math
1. A doughnut shop sell 30 kinds doughnut. In how many ways can you
(i) Get a bag of 12 doughnut?
(ii) Get a bag of 12 doughnut if you want at least 3 glazed doughnut and at least 4 raspberry doughnut?
(iv) Get a bag of 12 doughnut if you want exactly 3 glazed doughnut and exactly 4 raspberry doughnut?
2. Represent the following situation using type of function correspondence.
i. suppose the each worker in a group of employee(x) is assigned a job (y) from a set of possible jobs, each to be done by a single worker.
ii. In other situation,if every job there is a worker assigned job
iii On the other hand, when there is at least one job that has no worker assigned to it.

Explanation / Answer

(According to Chegg policy, only the first question will be answered if it has more than one subquestion. Please post the second question elsewhere)

1. (i)Since there are 30 kinds and a bag contains 12 doughnuts, total number of ways to get a bag

= 30C12

(ii) Since 3 glazed doughnuts and 4 raspberry dougnuts must be in the bag, we need to check for the remaining 5 doughnuts. These can come out of the 30 kinds of doughnuts.

Total number of ways = 30C5

(iii) Since 3 glazed doughnuts and 4 raspberry dougnuts are fixed, we need to check for the remaining 5 doughnuts. These can come out of the 28 kinds of doughnuts.

Total number of ways = 28C5

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