SOLUTION: In how many ways can 3 boys and 2 girls be arranged in a row if a selection is made from 5 boys and 4 girls? In how many of these arrangements does a boy occupy the middle position

Question 1149531: In how many ways can 3 boys and 2 girls be arranged in a row if a selection is made from 5 boys and 4 girls? In how many of these arrangements does a boy occupy the middle position?
Answer by Edwin McCravy(20054) (Show Source): You can put this solution on YOUR website!
In how many ways can 3 boys and 2 girls be arranged in a row if a selection
is made from 5 boys and 4 girls?

Choose the boys 5C3 ways
Choose the girls 4C2 ways
Place the boys in 5P3 ways
Place the girls in 2P2 ways

(5C3)(4C2)(5P3)(2P2) = (10)(6)(60)(2) = 7200 ways.

In how many of these arrangements does a boy occupy the middle position?

Choose the boy to occupy the middle position in 5C1 ways.
That leaves 4 positions to be filled with 2 boys and 2 girls
[from 4 remaining boys and 4 girls]
Choose the boys 4C2 ways
Choose the girls 4C2 ways
Place the 2 chosen boys in 2 of the 4 empty seats 4P2 ways
Place the 2 chosen girls in the remaining 2 empty seats 2P2 ways 

(5C1)(4C2)(4C2)(4P2)(2P2) = (5)(6)(6)(12)(2) = 4320 ways.

Edwin

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