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Contestants A, B, C, and D are in a 10K race. How many different ways can a race with 4 runners be completed? (Assume there is no tie.) In how many ways can A finish first and C finish second? What is the probability that A finishes first and C finishes second? Enter a reduced fraction or decimal.

Respuesta :

Using the arrangements formula and the probability concept, it is found that:

  • The race can be completed in 24 ways.
  • A can finish first and C second in 2 ways.
  • [tex]\frac{1}{12}[/tex] probability that A finishes first and C finishes second.

The number of possible arrangements of n elements is given by:

[tex]A_n = n![/tex]

A probability is the number of desired outcomes divided by the number of total outcomes.

In this problem, there are 4 runners, hence, the number of different ways the race can be completed is:

[tex]A_4 = 4! = 24[/tex]

Considering A first and C second, for the third and fourth positions, it is an arrangement of 2 elements, hence:

[tex]A_2 = 2! = 2[/tex]

The probability is:

[tex]p = \frac{2}{24} = \frac{1}{12}[/tex]

[tex]\frac{1}{12}[/tex] probability that A finishes first and C finishes second.

A similar problem is given at https://brainly.com/question/24648661

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