Question

Father has two apples, three pears, and two oranges. Every morning, during one week, he gives one fruit to his son for breakfast. How many ways are there to do this?

Answer 1

210

Explanation:

Since the condition does not state an opposite, I should assume that the apples are not distinguishable, same as the pears and the oranges.

So we have permutations of 7 fruits with 2 indistinguishable apples, 3 indistinguishable pears and 2 indistinguishable oranges.

The number of distinguishable arrangements is

7 1x2x3x4x5x6x7

--------- ---------------------- = 210

2x3x2 2x6x2

Answer. There are 210 ways to do it.