The problem is ambiguously worded. The "number of red balls" is a constant, R, so it is unlikely to ever coincide with K (irrespective of the value of N). What should be found here is
"the probability that, after N trials, the number of observations of red balls is K".
vectorization in N
Find nearest prime number less than input number
Magic is simple (for beginners)
02 - Vector Variables 5
Wind Chill Computation
A shooting competition
Simple polynomial evaluation
Probabilities - More brains than luck
Geometrical meaning of determinant
Non trivial identities - summation
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