If you want to divide a team of 10 people into teams A, B, and C of sizes 3,5, and 2, how many divisions are possible?
If you want to divide them into just teams of sizes 3,5, and 2, how many arrangements are possible?
I know that you use multinomial coefficients such that for part 1, the number of divisions is 10!/(3!5!2!) and for part 2, the number of divisions is 10!/(3!5!2!)/2!. I don't know why this is the case intuitively. Also, I can understand the formula for combinations as (n choose k) = (n*n-1*..n-k+1)/(k!) more clearly than (n!)/(k!)(n-k)!. I can't seem to interpret the second form of of the formula for combinations(or multinomials).