- #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?