# A soccer team has 10 victories, 4 losses and 7 ties throughout their season. In how many different orders can you receive these results?

Jan 21, 2018

$116396280$ways.

#### Explanation:

If someone were to ask you ," Hey, how many different ways are there to arrange $x$ things when they are all different?", you would simply calculate x!.

However, since there are total of 21 results, and some of them are identical to each other, we have to use another method.

The formula for such event is (n!)/(r_1!*r_2!...r_l!)
Instead of defining these variables, I will simply apply this to our problem.

First, there are total of 21 results. Therefore:
(n!)/(r_1!*r_2!...r_l!)=>(21!)/(r_1!*r_2!...r_l!)
Now, we know that there are 10 repeats of victories, 4 repeats of losses, and 7 repeats of ties.
Therefore, (21!)/(r_1!*r_2!...r_l!)=>(21!)/(10!*4!*7!)
We now calculate this to get:
(21!)/(10!*4!*7!)=116396280