A trade agreement was signed between 8 countries. If each country can form a par

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Question: A trade agreement was signed between 8 countries. If each country can form a partnership with every other country, how many unique partnerships can be formed?

Options:

Correct Answer: 28

Solution:

Number of unique partnerships = C(8, 2) = 8! / (2!(8-2)!) = 28.

A trade agreement was signed between 8 countries. If each country can form a par

Practice Questions

A trade agreement was signed between 8 countries. If each country can form a partnership with every other country, how many unique partnerships can be formed?

Questions & Step-by-Step Solutions

A trade agreement was signed between 8 countries. If each country can form a partnership with every other country, how many unique partnerships can be formed?

Step 1: Understand that we want to find out how many unique partnerships can be formed between 8 countries.
Step 2: Realize that a partnership involves choosing 2 countries from the 8 available countries.
Step 3: Use the combination formula C(n, r) to calculate the number of ways to choose r items from n items without regard to the order of selection. Here, n is 8 (the countries) and r is 2 (the countries in each partnership).
Step 4: The combination formula is C(n, r) = n! / (r!(n-r)!). For our case, it becomes C(8, 2) = 8! / (2!(8-2)!).
Step 5: Calculate 8! (which is 8 factorial) = 8 × 7 × 6 × 5 × 4 × 3 × 2 × 1.
Step 6: Calculate 2! (which is 2 factorial) = 2 × 1.
Step 7: Calculate (8-2)! = 6! = 6 × 5 × 4 × 3 × 2 × 1.
Step 8: Substitute these values into the combination formula: C(8, 2) = 8! / (2! × 6!).
Step 9: Simplify the equation: C(8, 2) = (8 × 7) / (2 × 1) = 56 / 2 = 28.
Step 10: Conclude that the number of unique partnerships that can be formed is 28.

Combinatorics – The study of counting, arrangements, and combinations, specifically using the combination formula to determine how many ways pairs can be formed from a set.
Combination Formula – The formula C(n, r) = n! / (r!(n-r)!) is used to calculate the number of ways to choose r elements from a set of n elements without regard to the order of selection.

A trade agreement was signed between 8 countries. If each country can form a par

What’s inside this PDF?

A trade agreement was signed between 8 countries. If each country can form a par

Practice Questions

Questions & Step-by-Step Solutions

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