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

1 Answer
Jan 21, 2018

Answer:

#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#