Question

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

Answer 1

that is 3 slots
12 in 1st slot
11 in 2nd
10 in 3rd

so that is 12*11*10 or 1320 ways

Answer 2

1320 ways

Explanation:

In a race in which twelve automobiles are entered and there are no ties.

We have to find the ways in which first three finishers come in.

In these questions when order is fixed means when first, second and third positions are fixed (First comes, then second and then third) then we use the permutation to find the number of ways.

3 positions out of 12 automobiles =
`^(12)P_(3)=(12!)/((12-3)!)`

=
`(12!)/(9!)`

=
`((12)(11)(10)(9!))/((9!))`

= 12×11×10

= 1320

In 1320 ways first three automobiles may come in.