Counting principle. Permutation and combination

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Counting principle:

If the set E contains n elements and the set F contains m elements, there are ways in which we can choose first an element of E and then element

of F.

Example:

We toss a coin two times. This experiment has two steps: the first step toss, the second toss. Each step has two outcomes: a head and a tail. Thus, total outcomes for two tosses of a coin= .

The four outcomes for this experiment are: HH, HT, TH, TT

Generalized counting principle:

Let be sets with elements, respectively. Then there are ways in which we can first choose an element of , then an element of ,……., and finally an element of .

Example:

How many outcomes does the experiment of throwing five dice have?

Solution:

Let , be set of all possible outcomes of die. Then . The number of the outcomes of the experiment of throwing five dice equals the number of ways we can first choose an element of , then an element of ,….. , and finally an element of .

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Читайте в этой же книге: Text I. | Text II. | Text IV. | LIST OF TERMS | Random experiment, outcomes, and sample space | Probability and its postulates | Formula for classical probability | Consequences of the postulates | Exercises | Probability rules |
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