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The Smith family has 4 sons and 3 daughters. In how many ways can they be seated in a row of 7 chairs such that at least 2 girls are next to each other?

 Dec 28, 2020
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Let's use complementary counting. The only way for no girls to be next to each other is if they sit b-g-b-g-b-g-b. There are 4!=24 ways to arrange the boys and 3!=6 ways to arrange the girls in this case. That makes 144 cases. There are 7!=5040 ways to organize the people with no restrictions so the answer is 5040-144=4896.

:D

 Jan 7, 2021

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