I have 10 balls(no distinction between them), i want to restribute all of them to 4 baskets(a basket can have them all and the others can be empty),so i care about counting how many ways i can put those balls into 4 baskets.
(basket1,basket2,basket3,basket4) some correct combinations are (0,10,0,0),(1,9,0,0),(1,1,1,7) and so on, is there some formula that can help me with that?
After some trial and error i thought about (k+n-1)!/n!(k-1)! which gives me (4+10-1)!/10!(4-1)! = 286 ways (is my thought correct?, if so why exactly?)
2nd question:what if i want basket number 4 to have ALWAYS at least 1 ball, i thought that possible ways to put balls from 10 balls to 1 basket is 10ways so i used above formula again to (now i have 3 baskets and at best case 9 people) (3+9-1)!/9!(3-1)! = 55ways meaning 55*10=550 ways.Is my thinking process correct?