In a race in which eleven automobiles are entered and there are no ties, in how many ways can the first three finishers come in?

990 ways

Step-by-step explanation:

The total number of automobiles we have is 11.

Now, what this means is that for the first position, we shall be selecting 1 out of 11 automobiles, this can be done in 11 ways (11C1 = 11! / (11-1) !1! = 11!/10!1! = 11 ways)

For the second position, since we have the first position already, the number of ways we can select the second position is selecting 1 out of available 10 and that can be done in 10 ways (10C1 ways = 10!9!1! = 10 ways)

For the third position, we have 9 automobiles and we want to select 1, this can be done in 9 ways (9C1 ways = 9!/8!1! = 9 ways)

Thus, the total number of ways the first three finishers come in = 11 * 10 * 9 = 990 ways