I need to find the number of ways to distribute six donuts of four kinds, such that each kind appears at least once. However, in this case, I cannot have any empty bins, since Bill needs to get at least one of each kind. So I need to modify the formula to account for this restriction. One way to do this is to first give each bin one object, and then distribute the remaining n-r objects freely. So the formula becomes (n-1) choose (r-1). In this problem, n is 6 and r is 4, so I plug them into the formula and get (6-1) choose (4-1) = 5 choose 3. I can calculate 5 choose 3 by using the formula n choose k = n!/(k!(n-k)!), where ! means factorial. So 5 choose 3 = 5!/(3!(5-3)!) = (5*4*3*2*1)/(3*2*1*2*1) = (5*4)/(2*1) = 10. Therefore, there are 10 combinations that satisfy Bill's order requirements. 
Bill is sent to a donut shop to purchase exactly six donuts. If the shop has four kinds of donuts and Bill is to get at least one of each kind, how many combinations will satisfy Bill's order requirements?