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?

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.