(Solution) - The binomial coefficient m k m k m k Describes the -(2025 Original AI-Free Solution)

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The binomial coefficient (m/k) = m!/(k! (m? k)!) Describes the number of ways of choosing a subset of k objects from a set of m elements
a. Suppose decimal machine numbers are of the form
±0.d1d2d3d4 × 10n, with 1 ? d1 ? 9, 0 ? di ? 9, if i = 2, 3, 4 and |n| ? 15.
What is the largest value of m for which the binomial coefficient
(m/k) can be computed for all k by the definition without causing overflow?
b. Show that (m/k) can also be computed by (m/k) = (m/k) (m - 1/k - 1) · · · (m ? k + 1/1)
c. What is the largest value of m for which the binomial coefficient (m/3) can be computed by the formula in part (b) without causing overflow?
d. Use the equation in (b) and four-digit chopping arithmetic to compute the number of possible
5-card hands in a 52-card deck. Compute the actual and relative errors.