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Hi Team 

My Doubt is conceptual in nature invoving more than two concept ,that is why i am asking here . Please help

get clarity on this , i would be extremely grateful .Please be assured that i have spent entire day podering over this and when i did not get it now at the end of the day i am troubling the team.

Doubt 1 : 

What is difference between two formula for partition , "  r^n  " and "  (n+r-1)! / (r-1)!  " ?

I believe that where arrangement is also required then later formula is used . Example : 5 Distinct Chocolate is distributed to 3 children , and it also matters order in which these chocolate is received by children then  "  (n+r-1)! / (r-1)!  " will be used. And if it  matters in how many ways children can get chocolate, no need for any order then "  r^n  " is used .

Please confirm whether i am right in my logic 

Doubt 2 :

What is purpose of diving by  " (r-1)!  " in formula  
(n+r-1)C(r-1)
and formula 
(n+r-1)!/(r-1)!

I could not think it through , my only guess is to remove duplicacy but i dont know how that duplicacy is formed .by (n+r-1)!

I know one logic explained in video that in case of repitition  (in example where 0 is chocolate and 1 is r ,i.e 00000100010000 ) , (r-1)  is represented by 1 and its repitative so to remove it ,we divide by (r-1)! as we do for repitition . 

But we can see in formula theory that   "r" is "DISTINCT"  means r is slots or boxes or children which are distinct so they can not be duplicate . 

Why is Formula divided by (r-1)! .

Thanks a ton for your time , waiting to hear from you soon.

Just last thing , my friend tells me i am putting unnecessary thoughts by diving  deep into how formula works . Please advice whether i am wasting my time as it is very time consuming to dig deep to roots and i am CA so no mathematical background after 12th so it is not possible for me to grasp working of formula of many topics as algebra and Number system 

I will be very grateful for your patience and time 

Animsh Kumar