Henry Ernest Dudeney/Modern Puzzles/167 - A General Election

Modern Puzzles by Henry Ernest Dudeney: $167$

A General Election

In how many different ways may a Parliament of $615$ members be elected if there are only $4$ parties:

Conservatives, Liberals, Socialists, and Independents?

You see you might have $\text C. 310$, $\text L. 152$, $\text S. 150$, $\text I. 3$;

or $\text C. 0$, $\text L. 0$, $\text S. 0$, $\text I. 615$;

or $\text C. 205$, $\text L. 205$, $\text S. 205$, $\text I. 0$; and so on.

The candidates are indistinguishable, as we are only concerned with the party numbers.

Sources

• 1926: Henry Ernest Dudeney: Modern Puzzles ... (previous) ... (next): Combination and Group Problems: $167$. -- A General Election
• 1968: Henry Ernest Dudeney: 536 Puzzles & Curious Problems ... (previous) ... (next): Combinatorial & Topological Problems: Miscellaneous Combinatorial Puzzles: $446$. A General Election