# Todai Entrance Exam: Math 2016 – Problem 3

**(1)** Distributing equivalent balls to distinguishable boxes is equivalent to choose balls from balls (first ball always go to first box). These chosen balls take the role of bars splitting remaining balls into boxes. So, the number of possible ways:

Reference for validation: Wikipedia

**(2)** This is the same as choosing balls from balls (combination):

**(3)** From (1), there are ways to distribute black balls into boxes and there are ways to distribute white balls into boxes. There are ways to arrange those boxes in the way such that a black box is followed by a white box and vice versa **(this sentence is wrong in the case that there are at least 2 boxes with the same number of balls)**. In conjunction with the formula in (2), we get:

**(4)**

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Working…

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