Step 1:
The probability of exactly three successes in a binomial experiment is given by the formula:
\[P(X=k) = C(n, k) \cdot (p)^k \cdot (1-p)^{n-k}\]
where \(P(X=k)\) is the probability of exactly \(k\) successes, \(C(n, k)\) is the number of combinations of
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