Henry Ernest Dudeney/Puzzles and Curious Problems/120 - Proportional Representation

Puzzles and Curious Problems by Henry Ernest Dudeney: $120$

Proportional Representation

In a local election, there were ten names of candidates on a proportional representation ballot paper.

Voters should place No. $1$ against the candidate of their first choice.

They might also place No. $2$ against the candidate of their second choice,

and so on until all the ten candidates have numbers placed against their names.

The voters must mark their first choice, and any others may be marked or not as they wish.

How many different ways might the ballot paper be marked by the voter?

Sources

• 1932: Henry Ernest Dudeney: Puzzles and Curious Problems ... (previous) ... (next): Arithmetical and Algebraical Problems: Various Arithmetical and Algebraical Problems: $120$. -- Proportional Representation
• 1968: Henry Ernest Dudeney: 536 Puzzles & Curious Problems ... (previous) ... (next): Arithmetical and Algebraical Problems: Miscellaneous Puzzles: $194$. Proportional Representation