20.
The sponsor of a local soccer tournament is responsible for writing an article for the local
paper announcing the 151, 2nd, and3rdplacewinners. If10teamsareinvitedtothe
tournament, and the sponsor wanted to get the article written in advance so it can go out
in the next morning's paper. how many different articles would she have to write to cover
all possibilities? The appropriate formula to use to solve this problem is:
a. Permutation
b. Binomial
c. Combination
d. Multiplication Counting Formula
e. None of the above.
The appropriate formula to use to solve this problem is the permutation formula. The permutation formula calculates the number of ways to arrange a specific number of objects from a larger set, where the order matters.
In this case, the sponsor is responsible for announcing the 1st, 2nd, and 3rd place winners out of 10 teams. Therefore, the order in which the teams are placed matters.
To calculate the number of different articles the sponsor would have to write, we can use the permutation formula:
nPr = n! / (n - r)!
Where n is the total number of objects (10 teams in this case) and r is the number of objects we select (3 winners in this case).
Plugging in the values, we get:
10P3 = 10! / (10 - 3)!
= 10! / 7!
= 10 * 9 * 8
= 720
Therefore, the sponsor would have to write 720 different articles to cover all the possibilities of announcing the 1st, 2nd, and 3rd place winners.
The correct answer is a. Permutation.