SOLUTION: Three boys: Andre, Boyd, and Charlie; and two girls: Deanna and Edith; are standing in line for lunch. If the boys and girls alternate in line, how many different ways could they

Question 250995: Three boys: Andre, Boyd, and Charlie; and two girls: Deanna and Edith; are standing in line for lunch. If the boys and girls alternate in line, how many different ways could they line up?
A.8 B.10 C.12 D.24 E.120

Answer by Edwin McCravy(20055) (Show Source): You can put this solution on YOUR website!
Three boys: Andre, Boyd, and Charlie; and two girls: Deanna and Edith; are standing in line for lunch. If the boys and girls alternate in line, how many different ways could they line up?
A.8 B.10 C.12 D.24 E.120


They must line up

Boy Girl Boy Girl Boy

Choose the first boy on the left any of 3 ways,
Choose the boy in the middle any of 2 ways, and
Choose the boy on the right just 1 way.
Choose the girl between the left boy and the middle boy either of 2 ways
Choose the girl between the middle boy and the right boy just 1 way.

That's 3x2x1x2x1 = 12 ways, choice (C).  Here they all are:

 1. ADBEC
 2. ADCEB
 3. BDAEC
 4. BDCEA
 5. CDAEB
 6. CDBEA
 7. AEBDC
 8. AECDB
 9. BEADC
10. BECDA
11. CEADB
12. CEBDA
 
Edwin

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