document.write( "Question 698550: A certain class has 6 girls and 5 boys. four of these students are to line up, with two girls on either end and two boys in between, how many such arrangements are possible? \n" ); document.write( "

Algebra.Com's Answer #430956 by Positive_EV(69) $\"\"$ $\"About$

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For this problem, you are selecting 2 girls from 6 to be at two positions in the line for girls, and selecting two boys from 5 to be at two positions in the line for boys. Since the order of the boys and girls in the line matters, calculate the values using permutations instead of combinations.
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\n" ); document.write( "\n" ); document.write( "The number of way to select k objects from n total objects when order is important is $\"nPk+=+n%21%2F%28n-k%29%21\"$ . The number of total arrangements is equal to the number of ways to select the 2 girls times the numbers of ways to select the 2 boys.
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\n" ); document.write( "\n" ); document.write( "There are $\"6P2+=+6%21%2F4%21+=+6%2A5+=+30\"$ ways to select the two girls are the ends of the lines and $\"5P2+=+5%21%2F3%21+=+5%2A4+=+20\"$ ways to select the two boys in the middle. The number of total orderings is thus 30*20 = 600. \n" ); document.write( "

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