3. again consider a little league team that has 15 players on its roster.

(a) how 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?

Step-by-step explanation:

a). 15C9 (you're choosing 9 players out of 15 players and the order of choosing does not matter) = 5005

b). 15C9 x 9! (you're choosing 9 players out of 15 and then you're arranging them for the batting order. when you arrange them for batting order, the order matters. so you have 9 choices for the 1st batting order, 8 choices for the second, and so on. you get 9!) = 450045

c). 5C3 x 10C6 (you're choosing 3 left handed players out of 5 left handed players and you're also choosing 6 right handed players out of 10 right handed players)= 10+210= 220

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