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
Calculate the area of a triangle between three points
Replace values under a limit
Non trivial identities - reshape
Area of polygon
Geometrical meaning of determinant
A shooting competition
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