Chapter 7.4, Problem 53E

### Finite Mathematics and Applied Cal...

7th Edition
Stefan Waner + 1 other
ISBN: 9781337274203

Chapter
Section

### Finite Mathematics and Applied Cal...

7th Edition
Stefan Waner + 1 other
ISBN: 9781337274203
Textbook Problem

# Itineraries Your international diplomacy trip requires stops in Thailand, Singapore, Hong Kong, and Bali. How many possible itineraries are there? [HINT: See Examples 1 and 2.]

To determine

To calculate: The number of possible itineraries if the trip requires stops in Thailand, Singapore, Hong Kong and Bali.

Explanation

Given Information:

The trip requires stops in Thailand, Singapore, Hong Kong and Bali.

Formula used:

The Decision Algorithm is to make a set of decisions to determine the number of possible outcomes.

A permutation of n items taken r at a time is an ordered list and the number of permutations is,

P(n,r)=nĆ(nā1)ĆāÆĆ(nār+1)

Calculation:

Consider the trip requires stops in Thailand, Singapore, Hong Kong and Bali.

There are 4 places in the trip and each itinerary is an ordered list.

Use the Decision Algorithm to make a set of decisions to determine the number of possible outcomes.

There are 4 empty slots and each itinerary is a list of 4 places chosen from Thailand, Singapore, Hong Kong and Bali.

Step 1: Choose a list from the 4 places.

Since, there are 4 empty slots and 4 places and it is an ordered list. Thus, Step 1 has P(4,4) choices

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