SOLUTION: 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?

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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?
Answer by Positive_EV(69) About Me  (Show Source):
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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.

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.

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.