Question

In horse racing, an exacta bet requires the bettor to pick the first two horses in the exact order. If there are 8 horses in a race, in how many ways could you make an exacta bet?

Short answer

In $56$ways we can make an exacta bet.

Step-by-step solution

Step 1. Given information

There are 8 horses in the race.

Exacta bet requires 2 horses in exact order.

Step 2. To find the number of ways of selecting two horses in the order.

The number of ways is:

$$\begin{gathered} P(8,2)=\frac{8!}{(8-2)!} \\ =\frac{8!}{6!} \\ =\frac{8\times 7\times 6!}{6!} \\ =8\times 7 \\ =56 \end{gathered}$$

So, there are 56 ways of making an exacta bet.