Question
How many are there to place 8 indistinguishable balls into four distinguishable bins?
The correct answer is
165
Allowing empty bins, distributions correspond to nonnegative integer solutions of \(x_1+x_2+x_3+x_4=8\). Stars and bars gives \(\binom{8+4-1}{4-1}=\binom{11}{3}=165\).
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Important Questions from Generating Functions - Teaching
The general solution of recurrence relation
\(a_r-5a_{r-1}+6a_{r-2}=4^r,\ r\ge2\) is:
Every bounded sequence has
How many bit strings of length ten either start with a 1 bit or end with two bits 00?
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