document.write( "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?\r
\n" ); document.write( "\n" ); document.write( "A.8 B.10 C.12 D.24 E.120
\n" ); document.write( "
\n" ); document.write( "

Algebra.Com's Answer #182887 by Edwin McCravy(20055)\"\" \"About 
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?
\n" ); document.write( "A.8 B.10 C.12 D.24 E.120
\n" ); document.write( "
\r\n" );
document.write( "They must line up\r\n" );
document.write( "\r\n" );
document.write( "Boy Girl Boy Girl Boy\r\n" );
document.write( "\r\n" );
document.write( "Choose the first boy on the left any of 3 ways,\r\n" );
document.write( "Choose the boy in the middle any of 2 ways, and\r\n" );
document.write( "Choose the boy on the right just 1 way.\r\n" );
document.write( "Choose the girl between the left boy and the middle boy either of 2 ways\r\n" );
document.write( "Choose the girl between the middle boy and the right boy just 1 way.\r\n" );
document.write( "\r\n" );
document.write( "That's 3x2x1x2x1 = 12 ways, choice (C).  Here they all are:\r\n" );
document.write( "\r\n" );
document.write( " 1. ADBEC\r\n" );
document.write( " 2. ADCEB\r\n" );
document.write( " 3. BDAEC\r\n" );
document.write( " 4. BDCEA\r\n" );
document.write( " 5. CDAEB\r\n" );
document.write( " 6. CDBEA\r\n" );
document.write( " 7. AEBDC\r\n" );
document.write( " 8. AECDB\r\n" );
document.write( " 9. BEADC\r\n" );
document.write( "10. BECDA\r\n" );
document.write( "11. CEADB\r\n" );
document.write( "12. CEBDA\r\n" );
document.write( " \r\n" );
document.write( "Edwin
\n" ); document.write( "
\n" );