# Can anyone confirm formula (combinations)

by uart
Tags: combinations, confirm, formula
 Sci Advisor P: 2,751 Hi, I've been scratching around trying to figure out a formula for the following problem and I've got one that I think is correct. Just wondering if anyone can confirm it for certain (like maybe you have it in a text book or know it well etc). Thanks. Problem : You need to partition n=k*m distinct objects into k sets each containing m objects. How many ways can you do this? Proposed Answer : Number of possible distinct partitionings = n! / ( k! * (m!)^k ) (I think it's correct).
 Emeritus Sci Advisor PF Gold P: 16,091 Sounds plausible.
 Sci Advisor HW Helper P: 9,396 Are the sets into which we partition indistinguishable? Ie if we partition n into n sets there are n! ways of doing this if we consider order, or just 1 if we say that they are all equivalent. I'm guessing fromyour formula order doesn't matter. So there are nCm ways of picking the first set, mutliplied by (n-m)Cm for the second and so on, but we need to divide by k! to forget the ordering which is, I suspect, exactly what your formula is.