Question

6) Provide an example of counting in your everyday life. Think of an example where you could use a counting method and describe the method.

Answer 1

Counting methods -

1) Permutation

2)Combinations

Combination. The total number of ways of selecting k distinct combinations of n objects, irrespective of order, (i.e., we are not ordering the items after we select k, but rather only doing the selection), is:

or as seen on calculators, [nCr]. This selection is called a “combination” to distinguish it from the permutation above.

Example: Pick 3 items from 10 in any order, where n = 10, k = 3. The total number of ways of making the selection is

k-Permutation. The number of ways of selecting and arranging k objects from among n distinct objects is:

or, as seen on calculators or written by hand, [nPk].

Example: pick 3 things from 10 items, and arrange them in order. In such a case, n = 10, k = 3, so the total number of overall outcomes, selections plus arrangements, is

Notice how, in this calculation, the fraction of very large numbers 10!/7! was greatly simplified by reducing it to (10)(9)(8). A simplification of this nature will always be possible when applying this rule or the below rule. There will always be a factorial in the numerator and a smaller factorial in the denominator, and the factors of a larger factorial always include a smaller factorial in its entirety.