Problem in solving Marbles

#1

I cannot find a way to solve this.
help required.

#2

We just need to use normal mathematical formula.
k=min(n-k,k-1);
for(int i=1;i<=k;i++)
{
ans=ans*(n-i)/(i);
}

Please have a look at this very short code. Its easy to understand.

#3

the for loop part is nCr calculation.

#4

but why do we decrement k and also n?

#5

We don’t decrease n. We minimize k.
Its better to calculate C(10,2) rather than calculating C(10,8).

#6

Okay i got you…
See, if we choose n balls, then k balls have to be of k different colours for sure.

We now have to select n-k balls with k types of options.
There is a general formula for this case (Using PnC) :
(n+r−1)! / (n−1)!⋅r!

Put the new value (n-k) instead of n in the mathematical formula to get the New formula for our question that equals to C(n-1,k-1).
I hope i am clear and you shall be able to implement the code :slight_smile:

#7

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