Question

(2.2.5) 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

Answer 1

Answer:

56 ways.

Step-by-step explanation:

This question is solved by using combinations and permutations chapters in the math book.

To put it simply, we need to find the number of 3 horse combinations we can make from 8 horses. This requires the combinations formula:

$C(n,r)=\frac{n!}{r!(n-r)!}$

here n is the total number of objects to choose from, and r is the number of objects we require in the combination or group.

Since there are 8 horses, n= 8

Since we need to choose only 3 of them, and order does not matter, r= 3

Solving the equation above using these inputs gives us 56 unique ways we can choose the three winners.