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Discrete Mathematics With Applicat...

5th Edition
EPP + 1 other
ISBN: 9781337694193

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BuyFindarrow_forward

Discrete Mathematics With Applicat...

5th Edition
EPP + 1 other
ISBN: 9781337694193
Textbook Problem
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Suppose the camera shop in exercise 4 can obtain at most tenA76 batteries but can get at least 30 of each of the other types.
a. How many ways can a total inventory of 30 batteries be distributed among the eight different types?
b. Suppose that in addition to being able to obtain only ten A76 batteries, the store canget only six of type D303. How many ways can a total inventory of 30 batteries be distributed among the eight different types?

To determine

(a)

The number of different selections of twenty pastries.

Explanation

Given:

The bakery is producing six different kinds of pastries and one of them is eclairs. Also, given that there are at least twenty pastries of each kind.

Formula used:

The number of the ways r objects can be selected from n categories of objects with repetition allowed is given by the formula (r+n1r).

Combination formula: (nm)=n!m!(nm)!.

Calculation:

It is given that there are 6 different kinds of pastries and there are at least 20 pastries of each kind. It has been asked to make selection of 20 pastries.

So, it gives n=6 and r=20. Now, use the formula to find the possible selection as shown below.

( r+n1 r)=( 20+61

To determine

(b)

The number of different selections of twenty pastries if at least three must be eclairs.

To determine

(c)

The number of different selections of twenty pastries which contains at most two eclairs.

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