I assume you mean circular races; I can’t think of any significant value add I could provide in that 😦 Just the standard fare ou would find in any concept-book. If I do, rest assured I will post.
Sir, what if in the first question..if 20 people were seated in a “circle” and we had to select 3 such that none of them are next to each other? Could you plz explain this scenario?
I’ll try to do a post on that situation at some point, though it is probably comfortably out of CAT scope. But basically, the thought process for selecting 3 seats out of 20 in a circle would be like: you select 3 seats, put 3 in between, and then put the other 14 in the 3 gaps in 16C2 ways. For people, slightly messier, I think one could make cases to be safe.
Hi J,
Please reply if there is anything wrong with my understanding. In the 1st ques, we are taking 5 regions as there can be 5 places(including the possibility of a chair before the first and after the last resp.) between the 4 chairs (i.e we are taking the 7 chairs as a single entity and dividing them in the rest ). Had it been given if one of the chairs was the last one or the first one , then we would have to partition in 4 regions as now there would be 4 possibilities (deducting one which would have come before first or last.)
Yes that is exactly right. Think of it as equivalent to distributing 16 chocolates to 5 kids such that only the corner ones can go away empty-handed. We would give the middle 3 kids 1 chocolate each and then distribute the remaining 13 among all 5 kids with no conditions whatsoever.
the second question from previous post which is solved here in a different approach of keeping at least 3 people in between them, so while of arranging 15 people, why we took 3 partitions only? shuldn’t it be 6? or we have considered those 3 as a single entity?
Hi J,
Here we are talking in terms of chairs which are identicals, but people sitting on it are not. So don’t you think there will be some permutation also.
We want to select 4 people, not arrange them. So choosing 4 chair numbers is sufficient. Remember that chairs are identical but chair positions are not!
Not clear with the wording of the train stops question. “How many ways the train can stop in 5 stations which aren’t consecutive”, then what exactly are those 7 stops?
The 5 stops and the start and end points of the track (basically, the wording indicates that between the starting station and the first of the five stations also there has to be a gap)
CAT-holics 
I didn’t understand after you placed 7 chairs.
Read the earlier PnC posts (specifically the ones on Theory of Partitioning)
regards
J
Could you post on Circular Motion Concepts in the CAT lead up?
I assume you mean circular races; I can’t think of any significant value add I could provide in that 😦 Just the standard fare ou would find in any concept-book. If I do, rest assured I will post.
regards
J
Sir, what if in the first question..if 20 people were seated in a “circle” and we had to select 3 such that none of them are next to each other? Could you plz explain this scenario?
I’ll try to do a post on that situation at some point, though it is probably comfortably out of CAT scope. But basically, the thought process for selecting 3 seats out of 20 in a circle would be like: you select 3 seats, put 3 in between, and then put the other 14 in the 3 gaps in 16C2 ways. For people, slightly messier, I think one could make cases to be safe.
regards
J
Hi J,
Please reply if there is anything wrong with my understanding. In the 1st ques, we are taking 5 regions as there can be 5 places(including the possibility of a chair before the first and after the last resp.) between the 4 chairs (i.e we are taking the 7 chairs as a single entity and dividing them in the rest ). Had it been given if one of the chairs was the last one or the first one , then we would have to partition in 4 regions as now there would be 4 possibilities (deducting one which would have come before first or last.)
As always,thanks for the post. 🙂
Yes that is exactly right. Think of it as equivalent to distributing 16 chocolates to 5 kids such that only the corner ones can go away empty-handed. We would give the middle 3 kids 1 chocolate each and then distribute the remaining 13 among all 5 kids with no conditions whatsoever.
regards
J
the second question from previous post which is solved here in a different approach of keeping at least 3 people in between them, so while of arranging 15 people, why we took 3 partitions only? shuldn’t it be 6? or we have considered those 3 as a single entity?
Hi J,
Here we are talking in terms of chairs which are identicals, but people sitting on it are not. So don’t you think there will be some permutation also.
Regards,
S
We want to select 4 people, not arrange them. So choosing 4 chair numbers is sufficient. Remember that chairs are identical but chair positions are not!
regards
J
Not clear with the wording of the train stops question. “How many ways the train can stop in 5 stations which aren’t consecutive”, then what exactly are those 7 stops?
The 5 stops and the start and end points of the track (basically, the wording indicates that between the starting station and the first of the five stations also there has to be a gap)
regards
J