the organizer of a television show must select 5 people to partipate in the show. the participants will be selected from a list of 30 people who have written in to the show. if the participants are selected randomly, what is the probability that the 5 youngest people will be selected?

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To find the probability of selecting the 5 youngest people out of a group of 30, we need to determine the total number of possible outcomes and the number of favorable outcomes.

Total Number of Outcomes:
The total number of possible outcomes is the total number of ways to choose any 5 participants from a group of 30. This can be determined using the combination formula, also known as "n choose k", which is calculated as:

n! / (k! * (n - k)!)

Where n is the total number of items and k is the number of items chosen. In this case, n = 30 (total number of people) and k = 5 (number of participants to be chosen).

Total Number of Outcomes = 30! / (5! * (30 - 5)!)

Favorable Outcomes:
Since we want to choose the 5 youngest people, we need to determine how many ways we can choose 5 participants from the 5 youngest people in the group of 30. This can also be calculated using the combination formula:

Favorable Outcomes = 5! / (5! * (5 - 5)!)

Calculating the Probability:
Finally, we can calculate the probability by dividing the number of favorable outcomes by the total number of outcomes:

Probability = Favorable Outcomes / Total Number of Outcomes

Substituting the values we calculated:

Probability = (5! / (5! * (5 - 5)!)) / (30! / (5! * (30 - 5)!))

Simplifying:

Probability = (5! / 5!) / (30! / (5! * 25!))

Probability = 1 / (30 * 29 * 28 * 27 * 26)

Calculating:

Probability ≈ 0.00008611

Therefore, the probability that the 5 youngest people will be selected randomly is approximately 0.00008611, or about 0.0086%.

To calculate the probability of selecting the 5 youngest people from a list of 30 individuals randomly, we need to determine the total number of possible outcomes and the number of favorable outcomes.

Total number of possible outcomes:
Since the participants will be selected randomly, the order in which they are selected does not matter. Therefore, we can calculate the total number of possible outcomes using the combination formula: nCr = n! / (r!(n-r)!), where n is the total number of people (30) and r is the number of people to be selected (5). So, the total number of possible outcomes is:

Combination of 30 people selected 5 at a time: 30C5 = 30! / (5!(30-5)!) = 142506

Number of favorable outcomes:
The 5 youngest people need to be selected, so there is only 1 way for this to occur.

Probability (P) = Number of favorable outcomes / Total number of possible outcomes

P = 1 / 142506 ≈ 0.000007

Therefore, the probability that the 5 youngest people will be selected randomly is approximately 0.000007, or 0.0007% chance.