Question

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

Answer 1

`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`