Use the Fundamental Counting Principle
Solve the problem.
-In how many ways can 7 players be assigned to 7 positions on a baseball team, assuming that any player can play any position?
A)5040 ways
B)2520 ways
C)10,080 ways
D)42 ways

Question

Quizplus · Accepted Answer

The Fundamental Counting Principle states that if there are m ways to do one thing and n ways to do another, then there are m x n ways to do both. In this problem, there are 7 players who can be assigned to any of the 7 positions, so there are 7 options for the first player, 6 options for the second player (since one position has been filled), 5 options for the third player, and so on until there is only one player left to be assigned to the remaining position. This can be represented as 7 x 6 x 5 x 4 x 3 x 2 x 1, which simplifies to 5040 ways. Therefore, the best choice is A) 5040 ways.