Again consider a Little League team that has 15 players on its roster. a.? ow many ways are there to select 9 players for the starting lineup? b. ?How many ways are there to select 9 players for the starting lineup and a batting order for the 9 starters? c. Suppose 5 of the 15 players are left-handed. How many ways are there to select 3 left-handed outfielders and have all 6 other positions occupied by right-handed players?

Answer: Step 1 of 1 Given, Little League team that has 15 players on its roster. a. Selecting 9 players for the starting lineup 15! Total number of ways 15C =9 9!(15 9) ! = 5005 Therefore, there are 5005 ways to select 9 players for the starting lineup. b. Selecting 9 players for the starting lineup and a batting order for the 9 starters 15! Total number of ways 15P =9 (15 9)! = 1816214400 Therefore, there are 1816214400 ways to select 9 players for the starting lineup and a batting order for the 9 starters. c. Suppose 5 of the 15 players are left-handed. Select 3 left-handed outfielders and have all 6 other positions occupied by right-handed players. Total number of ways = 5P × 10P 3 6 = 60 ×151200 = 9072000 Hence, there are 9072000 ways to select 3 left-handed outfielders and have all 6 other positions occupied by right-handed players.