Yummy
Probability
Level
3
In the pastry shop they make 4 types of cakes: chocolate muffins, brownies, cheesecake and coffee cake. How many ways there are to buy 7 cakes?
The answer is 120.
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1 solution
Let us buy : a choco-muffin cakes, b brownies, c cheese cakes, d coffee cakes.
Then a + b + c + d = 7 Note that a, b, c & d have to be non-negative integers.
This is equivalent to distributing 7 chocolates to 4 children, such that one or more of them get 0 chocolates.
Total number of ways of doing this is [ 7 + 4 - 1 ] C [ 4 - 1 ]