You are running a year-end bonus pool for your top credit analysts. You have 10 analysts, and you wish to recognize the top 3. How many different possible outcomes are there, if all three get the same bonus? How many different outcomes are there if the top analyst gets 50% of the bonus pool, the second best analyst gets 30%, and the third best gets 20%?
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A. B. C. D.C
The combination, or binomial formula, gives the number of ways that k objects can be chosen from n items, without regard to the order of choosing. The formula is n_C_k = (n choose k) = n! / [k! *(n-k)!]. In this case, we have (10 choose 3) = 10! / [3! * 7!] = (10
* 9 * 8) / (6) = 120. In the second case, where the order chosen does matter, we need the general permutation formula, which gives the number of ways that k objects can be chosen from n items, with regard to order. The formula is n_P_k = n! / (n- k)!. Here, it is 10! / (10-3)! = 720. For permutations, we don't consider choosing analysts 3, 7, and 6 the same as choosing analysts 7, 3, and 6, so there are more combinations than under the combination formula.