In a group of 40 friends attending a concert, they occupy a single row. Among them, there are eight pairs who wish to sit next to each other.

How many distinct arrangements can the friends have while ensuring each pair sits together?

Answer Choices

Correct answer marked below

32!*8

32!*16

32!*2^8

Correct

33!*8!

32!*8!*2^8

See the full step-by-step explanation

You can see the correct answer above. Sign in for free to unlock the complete worked solution.

Track your performance and improve

Get detailed analytics, unlock full explanations, and move up difficulty tiers as you practice.

Start for free Sign in

Explanation

Preview

Official Explanation

Official

To solve this problem, we treat each of the eight pairs as a single unit or block. This means we have 32 units to arrange (the 32 individual friends plus the 8 pairs). The number of ways to arrange these 32 units is…

Read the full explanation

Create free account Sign in

Comments

DangApr 19, 2025

thanks!

AnkitJan 14, 2025

still struggling with these types of problems

MotolaniJun 18, 2024

thanks for taking time to upload it!

What this question tests

What it tests

Whether you can count arrangements and selections correctly — permutations vs. combinations.

Common trap

Overcounting: treating a selection as ordered when order does not matter, or forgetting to divide by duplicates.

In a group of 40 friends attending a concert, they occupy a single row. Among them, there are eight pairs who wish to sit next to each other.How many distinct arrangements can the friends have while ensuring each pair sits together?