Combination Question

Q:

In how many ways can 8 white and 4 black draughtsmen can be arranged in a pile?


I am having difficulty with this. I do not know where to start

8 w 4 b

in a pile so does it mean one for after the other like layering one brick onto of another one
my problem is it does not say how many spaces in a pile so i am confused

please can i have some direction
thank you

Q:

In how many ways can 8 white and 4 black draughtsmen can be arranged in a pile?


I am having difficulty with this. I do not know where to start

8 w 4 b

in a pile so does it mean one for after the other like layering one brick onto of another one
my problem is it does not say how many spaces in a pile so i am confused

please can i have some direction
thank you

There are 12 in total. So there are 12! different arrangements.

But considering 8 whites are indistinguishable, and 4 blacks are indistinguishable, you need to adjust your answer accordingly.

Think of just one colour and how many positions can be allocated to each counter of that colour.

Edit: I think they mean a stack of12 counters with different orderings of the white and black counters. No spaces.

thank you for the help but the problem I am having is using combinations to answer it
but using permutations the answer is
but I dont see how to use combinations to answer this question

there are 12 spaces _ _ _ _ _ _ _ _ _ _ _ _
Now if I put the blacks this way
B _ _ B _ _ B _ _ B _ _
there are 8 spaces and if i choose 8 of the whites to fill in the spaces thus; 8C8 = 1

is there any way to do this using combinations theory only?

thank you for the help but the problem I am having is using combinations to answer it
but using permutations the answer is
but I dont see how to use combinations to answer this question

there are 12 spaces _ _ _ _ _ _ _ _ _ _ _ _
Now if I put the blacks this way
B _ _ B _ _ B _ _ B _ _
there are 8 spaces and if i choose 8 of the whites to fill in the spaces thus; 8C8 = 1

is there any way to do this using combinations theory only?