q34

[Saumyojit]

Seven different objects must be divided among three people. In how many ways can it be done if one or two of them can get no objects?​

One person get no objects : selecting that one person out of 3 -> 3c1 ; To make sure other two person get atleast one i give them two (one each) 7c2 *2! ; Now remaining 5 objects which is to be shared btwn those two
A b c d e Partition --> 6c1 . So , 3c1 * 7c2 * 2 ! * 6c1= 756

Case 2: Two person get no objects -> 3c2

Where am i wrong?

 

[Dr.Peterson]

Seven different objects must be divided among three people. In how many ways can it be done if one or two of them can get no objects?

I would interpret this not to mean that either 1 or 2 of the people get no objects, but that no more than two can. The word "can" doesn't mean "must", so this allows for none of them getting no objects. (Note that it is impossible for all three to get no objects!) So all this means is that any of the people might get none. On the other hand, I could well be wrong about that, because once again the language is awkward.

So I think you are making it too difficult. Just decide who gets each object.

Once again, please show the entire problem, including choices, which are useful for checking our interpretation and the format required for the answer.

Oh ... also, shouldn't this be q35, as we already have a q34?

 

[pka]

Seven different objects must be divided among three people. In how many ways can it be done if one or two of them can get no objects?
One person get no objects : selecting that one person out of 3 -> 3c1 ; To make sure other two person get atleast one i give them two (one each) 7c2 *2! ; Now remaining 5 objects which is to be shared btwn those two
A b c d e Partition --> 6c1 . So , 3c1 * 7c2 * 2 ! * 6c1= 756

If [imath]A~\&~B[/imath] are two finite sets and [imath]\mathcal{F}=\{f| f:A\to B\}[/imath] them [imath]\|\mathcal{F}\|=\|B\|^{\|A\|}[/imath].
There are [imath]3^7[/imath] functions from a set of seven to a set of three. How would we adjust the mappings to answer this question?

[imath][/imath][imath][/imath][imath][/imath]

 

[Saumyojit]

The word "can" doesn't mean "must", so this allows for none of them getting no objects.

Most of p & c question depends on English . yes i should have picked up on that word "can".
It means it is not necessary that in all the arrangements I have to ensure one or two person receives no objects but in SOME arrangement it CAN happen.
Yes , 3^7