Question

tony is promoting his bands first concert. he contacts 10 local radio stations. if 4 of them agree to interview him on the air, what is the probability they are the top 4 stations in the area?

Answer 1

The probability that the 4 stations that agree to interview Tony are the top 4 stations in the area is 1 / 5040.

Step-by-step explanation:

The probability that the 4 stations that agree to interview Tony are the top 4 stations in the area can be calculated using the concept of permutations. There are a total of 10 local radio stations and we want to find the probability of selecting the top 4 stations out of the 10 available stations.

The number of ways to select 4 stations out of 10 is given by the formula: nPr = n! / (n - r)! = 10! / (10 - 4)! = 10 x 9 x 8 x 7 = 5040, where n is the total number of stations and r is the number of stations to be selected.

The probability of selecting the top 4 stations out of the 10 available stations is therefore: 1 / 5040.

Answer 2

The probability that the 4 local radio stations agreeing to interview Tony are the top 4 stations in the area is calculated by considering one specific combination over the total number of ways any 4 stations can be selected, which yields a probability of 1/210.

Step-by-step explanation:

The student is essentially asking for the probability of a specific event occurring under the condition that there are multiple possible outcomes, which is a typical problem in the area of combinatorics and probability in mathematics.

To find the probability that the 4 stations agreeing to interview Tony are the top 4 stations, we need to consider the number of ways this specific selection of 4 stations can occur compared to the total number of ways any 4 stations can be selected.

Since there is only one way to choose the top 4 stations, and there are combinations of 10 stations taken 4 at a time, the formula for which is 10C4 (which is equal to 210), the probability is:

P(top 4) = 1 / 10C4 = 1 / 210

Thus, the probability they are the top 4 stations is 1/210.