Event A: The first three prize winners are Kira, Ravi, and Soo, regardless of order.

The total number of ways to select 3 winners out of 7 people is given by the combination formula C(n, r) = n! / [(n-r)!r!], where n is the total number of people, r is the number of winners, and "!" denotes factorial.

So, the total number of ways to select 3 winners out of 7 people is C(7, 3) = 7! / [(7-3)!3!] = 35.

Since the order of the winners does not matter in Event A, there are 3! = 6 ways to arrange Kira, Ravi, and Soo as the winners.

Therefore, the probability of Event A, denoted as P(A), is the number of favorable outcomes (the number of ways to arrange Kira, Ravi, and Soo as the winners) divided by the total number of outcomes (the total number of ways to select 3 winners out of 7 people).

So, P(A) = 6 / 35 = 6/35 = 2/15.

Event B: Ravi is the first prize winner, Soo is second, and Elsa is third.

The total number of ways to select 3 winners out of 7 people in a specific order is given by the permutation formula P(n, r) = n! / (n-r)!, where n is the total number of people, r is the number of winners, and "!" denotes factorial.

So, the total number of ways to select 3 winners out of 7 people in a specific order is P(7, 3) = 7! / (7-3)! = 210.

Since the order of the winners matters in Event B, there is only 1 way to arrange Ravi, Soo, and Elsa as the first, second, and third winners, respectively.

Therefore, the probability of Event B, denoted as P(B), is the number of favorable outcomes (the number of ways to arrange Ravi, Soo, and Elsa as the first, second, and third winners, respectively) divided by the total number of outcomes (the total number of ways to select 3 winners out of 7 people in a specific order).

So, P(B) = 1 / 210 = 1/210.

In conclusion, P(A) = 2/15 and P(B) = 1/210.

Question

Event A: The first three prize winners are Kira, Ravi, and Soo, regardless of order.

The total number of ways to select 3 winners out of 7 people is given by the combination formula C(n, r) = n! / [(n-r)!r!], where n is the total number of people, r is the number of winners, and "!" denotes factorial.

So, the total number of ways to select 3 winners out of 7 people is C(7, 3) = 7! / [(7-3)!3!] = 35.

Since the order of the winners does not matter in Event A, there are 3! = 6 ways to arrange Kira, Ravi, and Soo as the winners.

Therefore, the probability of Event A, denoted as P(A), is the number of favorable outcomes (the number of ways to arrange Kira, Ravi, and Soo as the winners) divided by the total number of outcomes (the total number of ways to select 3 winners out of 7 people).

So, P(A) = 6 / 35 = 6/35 = 2/15.

Event B: Ravi is the first prize winner, Soo is second, and Elsa is third.

The total number of ways to select 3 winners out of 7 people in a specific order is given by the permutation formula P(n, r) = n! / (n-r)!, where n is the total number of people, r is the number of winners, and "!" denotes factorial.

So, the total number of ways to select 3 winners out of 7 people in a specific order is P(7, 3) = 7! / (7-3)! = 210.

Since the order of the winners matters in Event B, there is only 1 way to arrange Ravi, Soo, and Elsa as the first, second, and third winners, respectively.

Therefore, the probability of Event B, denoted as P(B), is the number of favorable outcomes (the number of ways to arrange Ravi, Soo, and Elsa as the first, second, and third winners, respectively) divided by the total number of outcomes (the total number of ways to select 3 winners out of 7 people in a specific order).

So, P(B) = 1 / 210 = 1/210.

In conclusion, P(A) = 2/15 and P(B) = 1/210.

Knowee AI · Accepted Answer