How to calculate 4 dice combinations

Almogk4

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May 22, 2019
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As the headline says, I tried to figure it out and just couldn’t.
I want an easy formula or system to calculate how many different combinations without repeating numbers can I get from throwing four regular six sided dice.
 
Hello, and welcome to FMH! :)

I would approach this as follows:

For the first die, there are 6 choices, for the second there are 5 choices, for the third there are 4 choices and for the fourth there are 3 choices. So, using the fundamental counting principle, how many combinations does this give us?

Or equivalently, we can look at the number of ways to choose 4 from 6. What do you get?
 
I want an easy formula or system to calculate how many different combinations without repeating numbers can I get from throwing four regular six sided dice.
As MakFL points out you can simply use six choose three: \(\displaystyle \dbinom{6}{3}\).
\(\displaystyle \dbinom{N}{k}=\dfrac{N!}{k!\cdot(N-k)!}\). You may find this page useful.
 
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