- #1
kent davidge
- 933
- 56
Homework Statement
A man needs to buy 12 cars. There are 4 kinds available. He can buy any number of cars of each kind, the condition being 12 cars in total. In how many ways can he buy the 12 cars?
Homework Equations
The Attempt at a Solution
Hmmm as he can buy any number of each kind my guess is that this is not going to be a simple problem. Using only permutations will not be enough. If we let each kind of car be ##k_i##, then we have ##k_1 + k_2 + k_3 + k_4 = 12## and the problem reduces to finding all possible quadruples ##(k_1, k_2, k_3, k_4)## that satisfy that equation. It turns out that there are 455 possible ways of buying the 12 cars (book answer). How can I procceed?