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when three brand of juices are mixed in the ratio 3:4:5 and 4:5:6,the cost price of mixture of juices comes out to be rs 20 and 25 pr ltr respectively. find the cost price of litre of mixture of juices in which three brands are mixed in the ratio 6:7:8.

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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

Can you please explain the Example 2 discussed in the ratio an proportion video. Thank you

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