SOLUTION: There are two rows of seats in the classroom and each row has six seats. If a class has nine students, and among them three female students G1, G2 and G3 always sit in the first ro

Algebra ->  Permutations -> SOLUTION: There are two rows of seats in the classroom and each row has six seats. If a class has nine students, and among them three female students G1, G2 and G3 always sit in the first ro      Log On


   

Question 1160020: There are two rows of seats in the classroom and each row has six seats. If a class has nine students, and among them three female students G1, G2 and G3 always sit in the first row, two male students B1, B2 always sit in the second row. In how many different ways can all the nine students sit in the classroom?
Answer by Edwin McCravy(20054) About Me  (Show Source):
You can put this solution on YOUR website!
Seat the 3 girls in 3 of the 6 seats in the first row in 6P3 ways.
Seat the 2 boys in 2 of the 6 seats in the second row in 6P2 ways.
Seat the remaining 4 students in the remaining 7 seats in 7P4 ways. 

(6P3)(6P2)(7P4) = (120)(30)(840) = 3,024,000

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Here's looking at it a little different way.  Maybe you like this way better:

Let the 9 students be G1, G2, G3, B1, B2, S1, S2, S3, S4

Choose a seat for G1 in 6 ways.
Choose a seat for G2 in 5 ways.
Choose a seat for G3 in 4 ways.
Choose a seat for B1 in 6 ways.
Choose a seat for B2 in 5 ways.
Choose a seat for S1 in 7 ways.
Choose a seat for S2 in 6 ways.
Choose a seat for S3 in 5 ways.
Choose a seat for S4 in 4 ways.

6∙5∙4∙6∙5∙7∙6∙5∙4 = 3,024,000

Edwin