SOLUTION: A voice teacher selects 9 students from the class to sing for the trustees. The class has 12 men and 13 women. In how many ways can 9 students be selected and arranged in a row wit

Question 943342: A voice teacher selects 9 students from the class to sing for the trustees. The class has 12 men and 13 women. In how many ways can 9 students be selected and arranged in a row with 5 men in the middle and 2 women on each end?
Answer by Edwin McCravy(20054) (Show Source): You can put this solution on YOUR website!

Order matters, so we use permutations.  

13 women Position 4 = 13P4 

times

12 men Position 5 = 12P5

(13P4)(12P5) = (17160)(95040) = 1630886400.

---------------------------------
 
If you don't understand that, look at it this way:

They stand in this order:

W1,W2,M1,M2,M3,M4,M5,W3,W4

Choose W1 any of the 13 women.
Choose W2 any of the remaining 12 women.
Choose W3 any of the remaining 11 women.
Choose W4 any of the remaining 10 women.
Choose M1 any of the 12 men.
Choose M2 any of the remaining 11 men.
Choose M3 any of the remaining 10 men.
Choose M4 any of the remaining 9 men.
Choose M5 any of the remaining 8 men.

That's (13*12*11*10)*(12*11*10*9*8) = (13P4)(12P5) = (17160)(95040) = 1630886400 

Edwin

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