How many different ways can 12 unique artworks be allocated between two collectors – Alice and Bob – ensuring that both collectors receive an even number of artworks? (All artworks must be distributed.)

Answer Choices

Correct answer marked below

128

256

512

1024

2048

Correct

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 determine the number of ways to distribute 12 unique artworks between Alice and Bob while ensuring both receive an even number, we start by noting that each artwork can be given to either collector. This results in a total of

2^{12}

possible distributions. Since 12 is even, the…

Read the full explanation

Create free account Sign in

Comments

No comments yet

Be the first to share your thoughts and help others understand it better.

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.