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In horse racing, one can make a trifecta bet by specifying

Statistics for Engineers and Scientists | 4th Edition | ISBN: 9780073401331 | Authors: William Navidi ISBN: 9780073401331 38

Solution for problem 5E Chapter 2.2

Statistics for Engineers and Scientists | 4th Edition

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Statistics for Engineers and Scientists | 4th Edition | ISBN: 9780073401331 | Authors: William Navidi

Statistics for Engineers and Scientists | 4th Edition

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Problem 5E

In horse racing, one can make a trifecta bet by specifying which horse will come in first, which will come in second, and which will come in third, in the correct order. One can make a box trifecta bet by specifying which three horses will come in first, second, and third, without specifying the order.

a. In an eight-horse field, how many different ways can one make a trifecta bet?

b. In an eight-horse field, how many different ways can one make a box trifecta bet?

Step-by-Step Solution:

Step 1of 3:

In a horse racing, one can make trifecta  by specifying which horse will come in first, which will come in second, and which will come in third, in the correct order.one can make a box trifecta bet by specifying  which three horses will come in first, second, and third, without specifying the order. We have to find

(a)In an eight-horse field, how many different ways can one make a trifecta bet.

(b)In an eight - horse field, how many different ways can one make a trifecta box bet.

Step 2of 3:

Here in an eight-horse field one has to select the trifecta by specifying which three horses will come first.

So if there is N horses. If a person select one horse by claiming that it will come in the first position. Then he has (N-1) different choices to select a horse by claiming that it will come in the second position. Similarly he has (N-2) different choices to select a horse by claiming that it will come in the third position.

Since all this selection are independently the total possible ways to make a trifecta bet

                                                               

                                                                 =  N (N-1)

So in the case of eight horses one can make a trifecta = 876

                     

                                                                              = 336. Ways

That means in an eight horse field one can make a trifecta bet in 336 ways.

Step 3 of 3

Chapter 2.2, Problem 5E is Solved
Textbook: Statistics for Engineers and Scientists
Edition: 4
Author: William Navidi
ISBN: 9780073401331

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In horse racing, one can make a trifecta bet by specifying

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