Arrangement [closed]

Question

Number of ways we can arrange 5 books in 3 selves___________

Comments

Depends on books, identical or distinct

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https://gateoverflow.in/300636/madeeasy?show=300881

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update the test series name in the Title ! @srestha

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I'M not open that link

But I try to explain it in my way

5 books 3 selves 

3 selves act as a divide a 5 books  / how many ways we can do partition of 5 books 

It can be 4 | 1| 0 or 5 | 0 | 0 or 2  | 2 | 1 etc etc 

Now, if we want to divide 4 chocolate among 3 children --> 2 sticks needed for partition right ???

Now , same in this scenario think like we want to distribute 5 books among 3 children, so here we also need 2 partitions

$\binom{5+2}{2}$ 

Now we're just partitioning it , but question is 

we can arrange 5 books in 3 selves

Now we should arrange it by = $\binom{5+2}{2} X 5!$ = $\frac{7!}{2!}$ 

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i don't know why you don't have the powers of "EDITOR" after getting BOSS tag ? @magma

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no relation :p

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Magma if you want to become editor you have to mail to gatecse

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Dunno @Shaik Masthan brother :(

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in case of me, after attaining the BOSS tag, my privileges increases !

i thought there is a relation between them ! ( either you have >10k points or >365 days journey ) @Mk Utkarsh

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Shaik Masthan AFAIK there is no relation, i got 10k long back but i became editor few months ago 

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@Shaik

 u already updated with closing madeeasy tag na? otherwise I have to reopen 

@Magma

what should be condition for combination then?

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@srestha mam

I didn't get you point  ----> "what should be condition for combination then?"

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mam, no need right now, but next time on posting of the question should be take care ( i know o need to say to you but still,  forgive me if anything wrong )

 

what should be condition for combination then?

i didn't get what it means ?

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@Magma

I got ur point

actually we are arranging books but not two selves, that is why divide by 2.

but how do we know, selves are not distinct like upper selves and lower selves?

@Shaik Masthan

ok , I never mind :)

All the best for GATE to all of u:)

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actually we are arranging books but not two selves, that is why divide by 2.

It's not like that 

5 books 

You inserted 2 sticks between 5 books to make a partition of 3 

Total elements = 5+2  

Now you gave to only 2 students because whatever is left at last is gave to last students

Like 2 | 2 | 1 

Total 7 elements ( 5 books + 2 sticks )

Distribute to 2 child 

1st will get = 2 books

2nd will get = 2 books

And we didn't take care for what 3rd student will get 

Because whatever is left  after giving  to 1st and 2nd student we will gave it to 3rd student 

 

That's why 

From 7 elements we choose only 2 

$\binom{5+2}{2}$

 

Here all books are different that's why we multiply with 5! 

 

 

If all books are identical than it's =   $\binom{5+2}{2} X \frac{5!}{5!}$

 

" Sticks are only concept that we introduce to simply solve such questions " 

"If in this question it's given that books selves are also different " 

Than it has to be = 

$\binom{5+2}{2} X 5!  X 2!$

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@Magma

what will be ans

if they ask for

"Number of ways we can arrange 5 identical books in 3 children___________"