# algebra

posted by .

Find the number of ways the top four can finish in a race of nine people.

• algebra -

Assuming order matters, i.e.
A,B,C,D is counted differently as B,A,C,D.

There are 9 choices for the first place, 8 places for the second, 7 places for the third, and 6 places for the fourth. Applying the multiplication rule, there are 9*8*7*6 ways, or
P(9,4) [permutations]
=9!/(9-4)!

If order does not matter, the above must be divided by 4! combinations among the top four, or
number of ways
=C(9,4)
=9!/[(9-4]!4!]

## Similar Questions

1. ### math

There are nine customers waiting for their local SuperDuperMegaMart store to open on a big shopping day. In how many ways can the nine customers form a single line at the door?
2. ### algebra 2

Nine people are entered in a race. If there are no ties, in how many ways can the first three places be awarded?
3. ### algebra

three students are running a race .how different ways can they finish the race
4. ### physics

2 runners accelerate from rest to their top speeds. The 1st runner pat has an acceleration of 5.9 m/s^2 and reaches her top speed in 4 sec. The second runner steven accelerates at 4.4m/s^2 and takes 6.5 sec to reach his top speed the …
5. ### math

19 cars start a race. in how many ways can the top 3 cars finish
6. ### math

how many ways can 10 runners finish a race. 10 could finish 10 9 could finish 9 and so on would I times 10*9*8 ect that number seems way to big.
7. ### Statistics 220

suppose 59 cars start at a car race, how many ways can the top car finish the race?
8. ### Algebra

There are 15 people to choose from for a nine-person batting order in a baseball team. In how many ways can the people be arranged in the lineup?
9. ### Algebra

There are four cars entered into a pinewood derby race. In how many different orders can they cross the finish line?
10. ### Pre-Algebra

Here's the instructions for my portfolio: 1. Choose two animals with different speeds. You can choose fro m the chart that starts at the bottom of this page or do research to choose your own. 2. Design a fair race in which the two …

More Similar Questions