A baseball coach is creating a nine-player batting order by selecting from a team of 19 players.How many different batting orders are possible?
A)33,522,128,640
B)33,523,128,640
C)33,522,628,640
D)33,572,128,640
E)33,532,128,640

Question

A baseball coach is creating a nine-player batting order by selecting from a team of 19 players.How many different batting orders are possible? ​
A)33,522,128,640
B)33,523,128,640
C)33,522,628,640
D)33,572,128,640
E)33,532,128,640

Quizplus · Accepted Answer

The number of different batting orders is calculated using permutations since the order of selection matters. The formula for permutations is nPr = n! / (n-r)!, where n is the total number of items to choose from, r is the number of items to choose, and "!" denotes factorial. Here, n=19 (total players) and r=9 (players to choose for the batting order). Thus, the calculation is 19P9 = 19! / (19-9)! = 19! / 10! = 33,522,128,640.

A Baseball Coach Is Creating a Nine-Player Batting Order by Selecting