There are 5 locks and 5 keys and each of the 5 keys matches each of the 5 locks. What is the minimum and the maximum trial numbers of attempts needed to confirm that each of the 5 keys matches each of the 5 locks?

Answer Choices

Correct answer marked below

5,15

4,15

5,10

4,10

Correct

5,20

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

Assume you have locks 1-5 and keys A-E.

Minimum: assume you are lucky to find the correct key/combo on the first try. So, 1 -> A, 2 -> B, 3 -> C, and 4 -> D, then 5 must match with E. Therefore, you only need to try 4 combos at a minimum.

Maximum: assume that it takes as many guesses as possible. So, with the first key you try A, B, C, and D with no success, therefore E must be the match (so 4 attempts). For key 2 you no longer have E available so you try A, B, and C, with no success, therefore D must be the match (3 attempts). And so on for key 3 (2 attempts) and key 4 (1 attempt). Key 5 matches with the remaining lock for a total of 4 + 3 + 2 + 1 = 10 attempts.

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.