There are 32 students registered for this class 1.) How many different 9-player
ID: 3073471 • Letter: T
Question
There are 32 students registered for this class 1.) How many different 9-player batting orders could we choose for a softball team from the class? Explain how you computed this. 2.) How many 9-player teams could we choose, regardless of order? Explain how you obtained this number. 3.) Suppose our class challenged another class, with 15 students, to a softball game. What is the total number of ways both teams could choose their 9-player teams? Explain. There are 32 students registered for this class 1.) How many different 9-player batting orders could we choose for a softball team from the class? Explain how you computed this. 2.) How many 9-player teams could we choose, regardless of order? Explain how you obtained this number. 3.) Suppose our class challenged another class, with 15 students, to a softball game. What is the total number of ways both teams could choose their 9-player teams? Explain. 1.) How many different 9-player batting orders could we choose for a softball team from the class? Explain how you computed this. 2.) How many 9-player teams could we choose, regardless of order? Explain how you obtained this number. 3.) Suppose our class challenged another class, with 15 students, to a softball game. What is the total number of ways both teams could choose their 9-player teams? Explain.Explanation / Answer
1)
here for first position we have 32 choices ; for second 31 for third 30 and so on till we choose 9 players
=32*31*30*29*28*27*26*25*24=10178348544000 ( this is called permutation 32P9 )
2)as 9 people can be arranged in 9*8*7*6*5*4*3*2*1 =9! ways
therefore
P(number of ways to choose regardless of order) = 10178348544000/9! =28048800
( this is combination 32C9)
3)
number of ways =N(Choosing 9 from 32 of first class)*N(choosing 9 from 15 of second class)
=32C9 *15C9 =28048800*5005 = 140384244000
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