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Can anyone help plz?

 

A debate team consists of 5 freshmen and 4 sophomores.  (Everyone is distinguishable.)  In how many ways can they stand in line, so at least two of the sophomores are standing next to each other, and at least two of the freshmen are at the ends of the line?

 Feb 13, 2023
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there are 5*4 =20 ways to chose the 2 freshmem for the end of the line.   

 

Now there are 7! ways to order rest.  =  5040 ways

 

But how many of those 7! ways do NOT have any 2 sophomores standing together.

 

the order would have to be  SFSFSFS  there are 4!*3! = 144ways

 

5040-144 = 4896

 

4896*20 = 97920 ways

 Feb 13, 2023

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