A man wants to visit at least two of the four cities A, B, C and D. How many travel itineraries can he make? All cities are connected to one another.

Correct answer marked below

Correct

None of the above

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

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

Explanation

Preview

Official Explanation

Official

The number of ways to visit 2 cities when order matters =

P^2_4=\frac{4!}{(4-2)!}=12

: AB, BA, AC, CA, AD, DA, BC, CB, BD, DB, CD, DC.

The number of ways to visit 3 cities when order matters =

P^3_4=\frac{4!}{(4-3)!}=24

: ABC, ACB, BAC, BCA, CAB, CBA, ...…

Comments

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

What this question tests

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

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