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A managing committee consists of 12 expe...

A managing committee consists of 12 experts taken from three institutions x, y and z of which 5 from x, 4 from y and 3 from z. If three experts resign, then the probability that they belong to different institutions is `(k)/(11)`, then the value of `f(k)` is (where `f(k)=k^(3)-k^(2)+k+1`)

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