Help With a Particular Combination

[SlashKex]

Hi!

I am coming here from a video game(Warhammer 40k - Vermintide 2) and I would like some clarification with a combination(I believe it to be) related question.

In this game, there special enemies which differ from the normal ones. There are 8 of such enemies. These "specials" show up in different combinations/permutations. As you pump up the difficulty, the number of specials you can have coming for you at the same time increases, and you can also start getting multiple of the same kind. At the highest difficulty you can have up to 6 specials, 4 of the same, coming at you at the same time.

I have looked at combination/permutation equations but none that I've found shown me how to limit the number of repetitions per combination down to 4 as the game only allows 4 of the same special to show up at any one time and not 6.

Whilst I can see the difference the inclusion of repetition makes to the equation I simply do not know where to begin manipulating it to get to the right answer.

My questions is: What equation would you use to calculate how many combinations are possible from a pool of 8 specials when only 6 of them, 4 of the same, can be present at the same?

Thank you for the help in advance.

 

[Steven G]

1st of all your images are not equations as equations have an equal sign. What you have are formulas.

My questions is: What equation would you use to calculate how many combinations are possible from a pool of 8 specials when only 6 of them, 4 of the same, can be present at the same? I read what you wrote but it was confusing. However it seems to boil down to your final paragraph. I understand that there are a total of 8 specials where only 6 can appear at a time. Is it ALWAYS 6 that appear or up to 6 that can appear? There are always 4 that are the same? Are they always the same 4 or can there be a different set of 4? How many different sets of 4 can there be?

 

[joshuaa]

it is simple

do you care when the same [MATH]4[/MATH] came with different order?

if you care, use Combination with Repetition

if you don't care, use Combination without Repetition

 

[SlashKex]

1st of all your images are not equations as equations have an equal sign. What you have are formulas.

My questions is: What equation would you use to calculate how many combinations are possible from a pool of 8 specials when only 6 of them, 4 of the same, can be present at the same? I read what you wrote but it was confusing. However it seems to boil down to your final paragraph. I understand that there are a total of 8 specials where only 6 can appear at a time. Is it ALWAYS 6 that appear or up to 6 that can appear? There are always 4 that are the same? Are they always the same 4 or can there be a different set of 4? How many different sets of 4 can there be?

Is it ALWAYS 6 that appear or up to 6 that can appear? As I am unsure whether the game is hard-coded into filling up all 6 slots or not, let's go with the assumption that 6 specials will ALWAYS appear.

There are always 4 that are the same? No. FOUR of the same CAN appear but it is not guaranteed. I can get triple pairs thrown at me, a or one-one-one-three.

Are they always the same 4 or can there be a different set of 4? Same set of 4 can show up one after another but this is not guaranteed.

How many different sets of 4 can there be? EIGHT.