Table 2.
Worked-out example for the problem category “combination without replacement”.
| Example problem: Financial resources seem to be a key factor in mate choice, especially for women. Thus, it may be of interest that in the current top-200 list of the business magazine “Forbes” the 200 wealthiest people in the world are ranked by the sizes of their fortunes. What is the probability of selecting the 5 wealthiest persons out of this set of 200 people at random? |
| Please imagine this problem situation as well as possible and try to find a solution to the problem. When you have thought about the solution to this example problem please compare the solution that you have considered for this problem with this example solution. |
| Example solution: Combination problems are about the number of possibilities for selecting a subset of elements out of a set of elements without regard to the order in which they are selected (“combinations”). If no element can appear more than once in the selected subset, the problem is of the type combination without replacement. |
| The number A of possible combinations without replacement can be calculated by using the following formula: |
| A = n!/(n − k)!k! |
| n is the number of elements in a set that can be selected, k is the subset of selected elements and n! = n*(n − 1)*(n − 2)…*1. |
| The given example is about a selection out of a set of 200 persons (the top-200 list). This is the set of elements for selection (n = 200). The question asks the probability of randomly selecting the 5 richest persons out of this list, whereby the order of selecting the 5 persons is irrelevant. Therefore, the number of selected persons equals k = 5. |
| Inserting these values into the formula for combination without replacement, that is A = n!/(n − k)!k!, yields 200! / (200-5)! 5! = 2,535,650,040 combinations. |
| Thus the probability for one of these combinations (selecting the 5 wealthiest persons) equals 1/2,535,650,040 = 0.000000039%. |
Hyperlinks are underlined. The example problem and its solution were presented on separated pages.