Question

Question #a504d

Answer 1

10! or 3628800

Explanation:

First place can be filled in 10 ways second place in 9 ways third place in 8 ways...etc.

So we have 10 x 9 x 8 x 7 x 6 x 5 x 4 x 3 x 2 x 1 This can be written as 10! ( this is known as 10 factorial).

This idea can be a bit difficult to grasp at first.

These types of problems are called permutations.

The general formula for this is;

`(n!)/(( n - r )!)`

Where `n` is the number of objects and `r` is how many are taken at a time.

So above problem would be:

`(10!)/((10 - 10 )!)` = `(10!)/((0)!)`

Note: `0! = 1`

So we have: `10!` = 3628800

Hope this helps you.

Answer 2

`3,628,800` different ways.

Explanation:

There are `10` different possibilities for the 1 st runner.

For each of these `10` possibilities there are `9` different possibilities for the 2nd place runner. That is there are `10xx9 = 90` possibilities for the first 2 runners.

Similarly for each of these `90` possibilities there are `8` different possibilities for the 3rd place runner. That is there are `10xx9xx8=720` possible combinations for the first 3 runners.

Similarly there are `10xx9xx8xx7` possible combinations for the first 4 runners; and
there are `10xx9xx8xx7xx6` possible combinations for the first 5 runners; and
thethere are `10xx9xx8xx7xx6xx5` possible combinations for the first 6 runners; and
there are `10xx9xx8xx7xx6xx5xx4` possible combinations for the first 7 runners; and
there are `10xx9xx8xx7xx6xx5xx4xx3` possible combinations for the first 8 runners; and
re are `10xx9xx8xx7xx6xx5xx4xx3xx2` possible combinations for the first 9 runners; and
there are `10xx9xx8xx7xx6xx5xx4xx3xx2xx1` possible combinations for all 10 runners.

`10xx9xx8xx7xx6xx5xx4xx3xx2xx1=3,628,800`

Note that this is often written as: `10!` (read "10 factorial").
Most spreadsheets and some calculators have a built-in function for this, so you don't need to do the multiple calculations.