8 boys and 4 girls will be seated in two separate rows of 6 chairs each so that two specific girls are always together and no girls are in the same row. How many different positions can they take?
Two girls will always be together.
So, first, we choose one row for these two girls to sit in, ways = 2.
We can now choose 2 adjacent chairs in four different ways, and the girls can sit on them in 2 different ways.
Seating for these two girls is
All of the girls should not be in the same row, so at least one girl should be in a row separate from the remaining two girls.
So, from the remaining two girls, we choose one to sit in the second row, ways = 2.
Now, in the second row, we choose one of 6 chairs to seat the chosen girl, ways = 6.
Seating for the third girl is
The remaining nine can now be arranged in 9!
Therefore, the total number of ways is
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