434. Parliamentary Elections. How many different ways are there to elect 615 members of parliament if there are only four parties: Conservatives, Liberals, Socialists, and Independents? The mandates can be distributed, for example, as follows: Conservatives - 310, Liberals - 152, Socialists - 150, Independents - 3. Other distributions are also possible: Conservatives - 0, Liberals - 0, Socialists - 0, Independents - 615 or Conservatives - 205, Liberals - 205, Socialists - 205, Independents - 0, etc. We do not distinguish between candidates from each party, as only their total number is important to us.
434. There are 39147416 different ways in total. Add 3 to the number of members (which gives 618) and subtract 1 from the number of parties (which gives 3). Then the answer is the number of ways to choose 3 items from 618, that is,

\[
\frac{618 \times 617 \times 616}{1 \times 2 \times 3}=39147416 \text { ways }
\]

The general solution is as follows. Let \(p\) be the number of parties, and \(m\) be the number of members of parliament. The number of ways is equal to the number of combinations of \(m+p-1\) objects taken \(\mathrm{p}-1\) at a time.