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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 bakery produces six different kinds of pastry, one of which éclair. Assume there are at least 20 patries of each kind.

  1. How many different selection of twenty pastries are there?
  2. How many different selection of twenty pastries are there if at least three must be éclairs?
  3. How many different selection of twenty pastries contain at most tow éclairs?

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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