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karas teacher divides her class of 20 students into equally sized teams: the red,the yellow team, the green team, and blue team. she assigns each student to a team. what is the probability that kara is on red team

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Answer:

Explanation:

Since there are 4 equally sized teams and Kara is only assigned to one of them, the probability of Kara being assigned to the red team is:

Probability of Kara being on red team = Number of ways Kara can be on red team / Total number of possible outcomes

Number of ways Kara can be on red team = 20/4 = 5 (since each team has 5 students)

Total number of possible outcomes = Total number of ways of dividing 20 students into 4 teams

To find the total number of ways of dividing 20 students into 4 teams, we can use the formula for combinations:

Total number of possible outcomes = C(20,5) x C(15,5) x C(10,5) x C(5,5)

where C(n,r) represents the number of ways to choose r items from a set of n items.

Simplifying the expression:

Total number of possible outcomes = (20! / (5!15!)) x (15! / (5!10!)) x (10! / (5!5!)) x (5! / (5!0!))

Total number of possible outcomes = 15,504,000

Therefore, the probability of Kara being on the red team is:

Probability of Kara being on red team = Number of ways Kara can be on red team / Total number of possible outcomes

Probability of Kara being on red team = 5 / 15,504,000

Probability of Kara being on red team = 0.0000323 (rounded to 7 decimal places)

So the probability of Kara being assigned to the red team is approximately 0.0000323 or 0.00323%.

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