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.