Question: If 5 noble knights are to be seated at a round table, then how many different ways can they be seated?

1. 120
2. 96
3. 60
4. 35
5. 24

Answer:
Solution with Explanation:
Approach Solution (1):

There are 5! possibilities to arrange 5 things in a row.

But since it's a round table, shifting each object to one side and putting the last at the beginning again yields the same configuration. For each possible configuration there exist 5 such rotations, because it’s 5 objects, so you have to divide the number by 5:
5! / 5 = 4!
You can also approach it by just setting one object to be the first to avoid the rotation problem which directly yields to 4!, because it's 4 objects to arrange now.

Correct Option: E

Approach Solution (2):

If the seats are distinguishable (e.g. have numbers) then 5!=120 ways, the same as the number of ways they can be placed in a row.
If the seats are not distinguishable then each of the arrangements above is counted 5 times. This can be repaired by dividing by 5 and results in 5!/5=4!=24 possibilities.

Correct Option: E

Approach Solution (3):

It depends on how we interpret the question. Five people, named A, B, C, D, E, enter a restaurant. Any one of the 5 can sit in the first chair. Any one of the remaining 4 can sit to that person’s right. Then any of the remaining 3 to that person’s right, then any of the remaining 2 to that person’s right — and the last person takes the final chair. So: 5*4*3*2*1 = 120 arrangements. However, if it doesn’t matter how the five are rotated (as in: who sits with back to the wall, or looking out the window; that is: ABCDE = BCDEA), divide by 5, so 24 arrangements.

Correct Option: E

“If 5 noble knights are to be seated at a round table, then how many different ways can they be seated?”- is a topic of the GMAT Quantitative reasoning section of GMAT. This question has been taken from the book “GMAT Official Guide Quantitative Review”. To solve GMAT Problem Solving questions a student must have knowledge about a good amount of qualitative skills. The GMAT Quant topic in the problem-solving part requires calculative mathematical problems that should be solved with proper mathematical knowledge.

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