# Combinatorics: Seats in a parliament

• MHB
• Lancelot1
In summary, there are 3 possible ways to divide 400 seats between 3 parties in a parliament, with each party having at least one seat and no party having more than 200 seats. These possibilities are: 1) Party A: 200, Party B: 199, Party C: 1; 2) Party A: 199, Party B: 200, Party C: 1; 3) Party A: 200, Party B: 200, Party C: 0.
Lancelot1
Hello,

Another combinatorical question I scratch my head with.

In a parliament of a country there are 400 seats that should be divided between 3 parties.
What is the number of possibilities of division if we want that no party will have more than 200 seats ? Each party must have at least one seat.

The answer to this question is 3, since there are only 3 possible ways to divide the 400 seats among the three parties such that none of them has more than 200 seats:1) Party A: 200, Party B: 199, Party C: 1 2) Party A: 199, Party B: 200, Party C: 13) Party A: 200, Party B: 200, Party C: 0Hope this helps!

## 1. What is combinatorics?

Combinatorics is a branch of mathematics that studies the ways in which objects can be arranged, combined, and chosen from a larger set.

## 2. How does combinatorics apply to seats in a parliament?

In the context of seats in a parliament, combinatorics is used to determine the number of possible ways that members can be chosen and arranged within the parliament based on various criteria, such as political party or region.

## 3. What is the formula for calculating the number of possible seat combinations in a parliament?

The formula for calculating the number of possible seat combinations in a parliament is nCr = n! / (r!(n-r)!), where n is the total number of seats and r is the number of seats to be filled by a specific criteria.

## 4. How is combinatorics used in analyzing election results?

Combinatorics is used in analyzing election results by calculating the probability of different outcomes based on the number of seats, candidates, and voting patterns. It can also be used to identify potential voting blocs and predict potential alliances within a parliament.

## 5. Can combinatorics be applied to other political systems besides a parliament?

Yes, combinatorics can be applied to other political systems, such as legislative bodies, city councils, and even voting systems. It can also be used in other fields, such as computer science, genetics, and finance.

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