document.write( "Question 1119602: There are 6 people who will sit in a row but out of them James will always be left of Esther and John will always be right of Esther. In how many ways such arrangement can be done?\r
\n" ); document.write( "\n" ); document.write( "Note: i tried solving and got 24 as the answer but there was no 24 in the options. here are the options: \r
\n" ); document.write( "\n" ); document.write( "120
\n" ); document.write( "72
\n" ); document.write( "64
\n" ); document.write( "218.\r
\n" ); document.write( "\n" ); document.write( "Many thanks. \n" ); document.write( "
Algebra.Com's Answer #735192 by solver91311(24713)\"\" \"About 
You can put this solution on YOUR website!
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\n" ); document.write( "\n" ); document.write( "I know why you got 24 as an answer, and I know why that answer is incorrect. You apparently assumed that \"James will always be left of Esther and John will always be right of Esther\" meant that James is always to the IMMEDIATE left of Esther and that John is always to the IMMEDIATE right of Esther. However, that is not what the problem actually says. I'm sure there is a more elegant way of calculating this that I am missing, but here is how I came up with the answer:\r
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\n" ); document.write( "\n" ); document.write( "First, consider all possible arrangements where James is the very first person in the row from left to right and Esther is seated next to him:\r
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document.write( "J E J _ _ _ \r\n" );
document.write( "J E _ J _ _\r\n" );
document.write( "J E _ _ J _\r\n" );
document.write( "J E _ _ _ J\r\n" );
document.write( "
\r
\n" ); document.write( "\n" ); document.write( "Notice that for each of the above configurations, there are 6 different ways to arrange the other three people. Now move Esther one seat to the right:\r
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document.write( "J _ E J _ _  \r\n" );
document.write( "J _ E _ J _ \r\n" );
document.write( "J _ E _ _ J\r\n" );
document.write( "
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\n" ); document.write( "\n" ); document.write( "Again, for each configuration, there are 6 different ways to arrange the other three people. So continue on moving Esther one seat to the right until you run out of possibilities. Count the number of configurations and multiply by 6. If you do this carefully, you will obtain one of the numbers on your list.
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\n" ); document.write( "John
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\n" ); document.write( "My calculator said it, I believe it, that settles it
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