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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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A camera shop stocks eight different types of batteries, one of which is type A76. Assume there are at least 30 batteries of each type.
a. How many ways can a total inventory of 30 batteries be distributed among the eight different types?
b. How many ways can a total inventory of 30 batteries be distributed among the eight different types if the inventory must include at least four A76 batteries?
c. How many ways can a total inventory of 30 batteries be distributed among the eight different types if the inventory includes at most three A76 batteries?

To determine

(a)

To calculate:

The number of ways a batch of 30 batteries can be distributed among eight categories.

Explanation

Given information:

There are eight categories of batteries are available in a certain camera shop. Also, at least 30 units of each category are in the stock.

Formula used:

The number of ways to select r number of elements from a set of n elements is given by,

( r+n1r)=(r+n1)!(r+n1r)!×r!

Calculation:

It is needed to select an inventory of 30 individuals from eight different types and it is possible to select all units from one type or miss one or few types in the selection.

Here we have an unordered set of 30 elements with repetitions. Hence, we can use the formula for calculate the total number of possible ways

To determine

(b)

To find:

The number of possibilities to select inventory of 30 batteries representing all eight categories including at least 4 batteries from the category A76.

To determine

(c)

To find:

The number of possible ways to select a batch of 30 batteries including at most 3 batteries from the type A76 .

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