The number of possible combinations with a constraint

[Bayoudh101]

Hello , i was doing one of Euler project programming problems the other day , and i came across this one .
i tried everything i know about probability , i tried combinations and everything , and i just couldn't get something logically fit to solve this . i tried to ignore this but i just couldn't get it out of my head .

ignore the last line , as that can be done with the program .
for me this is a purely mathematical problem, all i tired to do was formulate p with k and n
i am just looking for the formula p(k,n) . it's giving me a headache .

thank you very much

 

[Stephen Tashi]

Approach it as: (number of ways to pick one of the n chips to have 3 defects)(number of ways to distribute k-3 defects among n chips)/ (number of ways to distribute k defects among n chips).

The number of ways to distribute d distinguishable defects among n distinguishable chips is $n^d$.

 

[Bayoudh101]

Approach it as: (number of ways to pick one of the n chips to have 3 defects)(number of ways to distribute k-3 defects among n chips)/ (number of ways to distribute k defects among n chips).

The number of ways to distribute d distinguishable defects among n distinguishable chips is $n^d$.

thank you very much sir , i can see it now .