The sponosor of a local soccer tournament is responsible for writting an article for the local paper announcing the 1st, 2nd, 3rd place winners.If 10 teamsare invited to the tournament, ans th sponsor wanted to get the article written in adance so it can go out in the next morning's paper, how many different article would she have to write to cover all possibilities? the appropriate formula to use to solve this problem is:
To calculate the number of different articles the sponsor would have to write to cover all possibilities, we can use the concept of permutations.
In this case, the sponsor needs to determine the 1st, 2nd, and 3rd place winners out of 10 teams. This forms a permutation problem because the order of the winners matters.
The appropriate formula to solve this problem is the permutation formula, which is given by:
P(n, r) = n! / (n - r)!
Where:
- P(n, r) denotes the number of permutations of selecting r items from a set of n items.
- n! represents the factorial of n, which is the product of all positive integers from 1 to n.
In this scenario, we need to find P(10, 3) since we are selecting 3 winners out of 10 teams.
Using the formula, we have:
P(10, 3) = 10! / (10 - 3)!
= 10! / 7!
Simplifying further:
10! = 10 × 9 × 8 × 7! = 10 × 9 × 8
Therefore:
P(10, 3) = (10 × 9 × 8) / 7!
= 720 / 5040
= 0.14285714285714285
So, the sponsor would need to write approximately 0.14285714285714285 different articles to cover all possibilities. Since you can't have a fraction of an article, you would need to round up to the nearest whole number.
Therefore, the sponsor would need to write 1 article to cover all possibilities.