Math Question!! 100 Meter Dash..??

Question

Four runners are lining up for the 100 meter dash. How many ways can the runners line up on the start line?

There are no multiple choice questions.

I have to show work.

Help?

Please and Thank You,

Chelse

Answer 1

There are 8 spots.

There are 4 people.

you just simply do 8X4

you should come up with 32 ways.

EDIT: (there are 8 spots on a track) if you are using 8 spots then use the work above.

If there is only 4 spots then use this:

4X4=16

4 spots

4 people

Answer 2

Short Cut:  Mutiply the 4 runners by the 4 spots = 16

Or use a tree diagram to show the combos.

Answer 3

You'll need to use a Permutation formula:

n_P_k = n! / (n - k)!

            

In this case n=4 runners and k=4 lines

4_P_4 = 4!/(4-4)! = 4x3x2x1 / 0! = 24/1 = 24

**Remeber 0 fatorial (0!) is defined as 1

You have 24 ways to arrange the runners (assuming 4 spots)

Answer 4

4! which is 4x3x2x1=24

easy huh?

you have four runners and four places. the first runner has four possibilities. the next one has only three possibilities and the third one 2 possibilities and the last runner has only one starting place.

I hope this helps you understand this type of problem  

Answer 5

Ok, let's say that the spot names are: s1, s2, s3, s4

And the runner names are: r1, r2, r3, r4

So on s1, we can have r1, r2, r3, or r4

And on s2 we can have r1, r2, r3, r4

On s3 we can have r1, r2, r3, r4

On s4 we can have r1, r2, r3, r4

So it looks like this,

s1, r1...s1, r2...s1, r3...s1, r4

s2, r1...s2, r2...s2, r3...s2, r4

s3, r1...s3, r2...s3, r3...s3, r4

s4, r1...s4, r2...s4, r3...s4, r4

So if you add them all up, you get 16 ways altogether..

I really hope I helped. I tried to explain it the best way I could.. I guess I kindof showed you a tree diagram, you know with all the combos and stuff..

Good luck!