doubt

[maahi]

if there is full stock of tennis balls on friday morning i.e 14 tennis balls cans and d stock was  sold out till sunday night then in how many ways could the balls have been sold on each day ?

[ankur]

This problem can be expressed in the similar way to this:
V(n,r)=number of ways to distribute r similar balls in n numbered boxes
or in this case number of ways in which 3 days can accomodate 14 balls.
V(n,r)=C(n-1+r,r)=(3-1+14,14)
=16C14=120

[maahi]

thank you so much :)
more problems :

1) an art collector owns 10 paintings by famous artists has to prepare a will , in how many ways can she leave d paintings to her three heirs.

[wolverine]

each of the painting can be given to any of the 3 persons
so no of ways wud be...3*3*3*3*3*3*3*3*3*3=3^10

[Sumit]

@Ankur: shouldn't it be V(n,r)=C(n-1+r,r-1)=(3-1+14,14-1)

[wolverine]

@sumit..i do think the same.

[maahi]

thanks
d formula u told is used when we have to select r objects from n categories with arbitrary repeats .
d formula given by ankur is used when n things have to be distributed among r people

[Sumit]

@maahi..still not agree...

[ankur]

@sumit I dnt knw which formula ur talking abt.,
nd why are you decreasing one.Plz go ovr the internet Im absolutely sure of the formula I have given
(Combinations with repetition.)

[ankur]

V(n,r)=C(n-1+r,r)=C(n-1+r,n-1)
Nt r-1..
No. Of ways we can distribute r similar balls in n numbered boxes..
n<r usually

[Sumit]

@Ankur: Got it!!!!!...this confusion arise coz u right.....'No. Of ways we can distribute r similar balls in n numbered boxes,......what usually mention in books is that No. Of ways we can distribute N similar balls in r numbered boxes..n the formula which I was applying is same as u...n+r-1Cr-1=n+r-1Cn (remember: this formulas I mention based on 'No. of ways to distribute n similar balls in r boxes which is just oppose of your definition....don't get confused like me...) you done it by latter one...I done it by former one...the replacement btw n & r made whole confusion...nothing else...