SOLUTION: Four people are selected at random. What is the probability that none of the people in this group were born on the same day of the week? (Round your answer to three decimal places.

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Question 1118593: Four people are selected at random. What is the probability that none of the people in this group were born on the same day of the week? (Round your answer to three decimal places.)

Answer by ikleyn(52800) About Me  (Show Source):
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Answer.  P = %287%2A6%2A5%2A4%29%2F7%5E4.

Solution

For each of the 4 people, write in a row his day of birth as the day of the week.


You will get the row of 4 integer numbers from 1 to 7 inclusively in each position.


The number of such different rows is  7%5E4.    <<<---=== It models the whole space of events.


The number of the rows with non-repeating numbers is  7*6*5*4.


The ratio is the probability under the question.