Assume a basket contains $n$ different types of balls, namely $1,2,3,\cdots,n$, and the number of balls for type $i$ is $m_i$ for $1\leq i\leq n$. If I can take out as many as all balls, or as least as no ball, how many different selections are possible?
I find that in the less general case in which there are $k$ different balls (i.e. any two balls are of different types), the number of possibilities is $2^k$, which is quite simple to calculate. However, I'm not able to figure out the formula for the general case above.
Please help me solve the question above!