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Counting principle. Permutation and combination

Читайте также:
  1. A) Practise using the words and word combinations in bold type to make other comparisons between some two-four regions of Russia. Write your best sentences down.
  2. B) Speak about the traffic in this country using the word combinations in bold type.
  3. C) Make up your own dialogues on choosing a career. Use the word combinations in bold type in them.
  4. I. Translate the following words and word combinations from Russian into English.
  5. II. Define the following words and word-combinations, use these lexical units in the examples of your own.
  6. II. Look through the text and find the words or word-combinations that mean the following, make up examples of your own with these words or phrases.

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 .

That is

 


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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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Exercises| Permutation

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