See , the question is slight ambiguous , with its wording so two case is arising however both would result A less than B. Here is why

Word: They should not sit next to one another

Case1: They should all not sit together , which means total - all 3 seating together = !7 - 6*!6 = !6

Case 2: They should not sit next to each other , meaning not even these two dudes sit together , all the three dudes separate from each other. That is possible when let these 3 dudes sit first and then fill the space (4 space would create in between them ) between them by the other 4 dudes . so !3 *!4

so in both the cases A is less than B

I believe A is greater. Can you provide link to this question?

ans is B, b results to 4320

Even I feel the answer is C;

Step 1 - Consider 7 people hence there are 7! ways to arrange.

Step 2- Now we have to take out the part(3 friends sitting together). So we can do like this

Consider 3 friends as 1 place, Hence now we have to arrange 4 people who are left out, but we have 3 friends as one so we have 5 people, we can say like that. hence 5!, but there is a catch we also have arrangement of 3 friends that is 3!. [(- - -) - - - -] { This is the pictorial representation of what I have done }

Step 3 - So for 3 people sitting together it will be 3! * 5! = 6 * 5! = 6!.

Step 4 - Final answer 7! - 6 !.

Hope this helps.

Matha noshto