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Exercise 6.1 The number of ways to select k unordered objects from n objects, for k = 1, 2,-.. n, is given by the binomial
Exercise 6.1 The number of ways to select k unordered objects from n objects, for k = 1, 2,-.. n, is given by the binomial coefficient C = ( ). It can be computed using two different schemes as described in the following IL (E6.la) (E6.1b) (a) Equation (E6.1a) represents the formal definition of C, which is straightforward to compute by using the MATLAB function factorial. Compute C for k = 10, n = 20.70, 120, 170, 200. TABULATE the results to show the variation of Cr with n. In particular, observe if numerical overflow occurs when n gets large. (b) To overcome the overflow problem, a recursive computational procedure based on (E6.1b) is suggested Specifically, an implementation of the recursive procedure involving the use of a for-loop is provided in the following: function C nk = bin coeff (n, k) C nk = n / k; for j -j initial jfinal c-nk c_nk * update-factor; = end Design the for-loop parameters j.intial, j.final and update factor. Then write a MATLAB function named binom.coeff to implement this recursive procedure. (c) Use the function binom.coeff to recalculate Ce for k = 10, n = 20.70. 120. 170. 200. Observe whether numerical overflow is an issue
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