Sir, why have you assumed fruits to be identical when it’s nowhere mentioned in the question. Aren’t we supposed to assume objects to be different if nothing is mentioned?
We have to apply common sense. People – distinct. Monkeys or parrots or elephants or fruits – identical (can you tell one apple from another or one monkey from another (unless you are the monkey-trainer of course). For most people, one apple is as good as another. They have to be specified distinct if you want to take them distinct.
sir in 2nd question, the two cases whivch are subtravted are the one with (5,0)-apples (6,0)- banana and (7,0)-chickoo simultaneously, and vice versa with (0,5) and (0,6) and (0,7) simultaneously, right? or is there something else..
In the second question with each person “at least” getting a fruit, how can we do it in terms of NCR? Give me a little hint please, not the complete answer as I want to think over it on my own. It’s kinda like a case of minimum one group not being empty, while so far we’ve done all groups not empty and the variant including the ones where empty groups are excluded too. How would we go about this problem with the theory of partitioning?
CAT-holics 
answer to your last paragraph –
6C2 * 7C2 * 8C2
Is it correct ?
Very probably 🙂
regards
J
Sir, why have you assumed fruits to be identical when it’s nowhere mentioned in the question. Aren’t we supposed to assume objects to be different if nothing is mentioned?
We have to apply common sense. People – distinct. Monkeys or parrots or elephants or fruits – identical (can you tell one apple from another or one monkey from another (unless you are the monkey-trainer of course). For most people, one apple is as good as another. They have to be specified distinct if you want to take them distinct.
regards
J
sir in 2nd question, the two cases whivch are subtravted are the one with (5,0)-apples (6,0)- banana and (7,0)-chickoo simultaneously, and vice versa with (0,5) and (0,6) and (0,7) simultaneously, right? or is there something else..
Absolutely correct.
regards
J
sir i think there is a printing mistake in 3rd answer as the 5,0 case is also shown as included..
You’re right, corrected! Thanks for pointing out…
regards
J
In the second question with each person “at least” getting a fruit, how can we do it in terms of NCR? Give me a little hint please, not the complete answer as I want to think over it on my own. It’s kinda like a case of minimum one group not being empty, while so far we’ve done all groups not empty and the variant including the ones where empty groups are excluded too. How would we go about this problem with the theory of partitioning?
Use partitioning to find all possible cases (bananas in 6C1 ways for example), then remove the two cases where someone goes empty-handed.
regards
J
Brilliant. Thanks, sir. I no longer fear PnC now 🙂