5. In how many ways can four boys and three girls be seated in a row con taining seven seats ( a ) if they may sit anywhere , (
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we have 4 gals, Stephanie, Andrea, Emily and Becca.
btw the end point should be (-6, -7) and the start point is (8, 6).
so, if we know the distance between those two points, we can just cut it in 4 equal pieces and each gal will be driving a piece.
now, Emily's turn is after Andrea, BUT, we had first Stephenie driving ¼ of the way, then Andrea driving ¼ of the way too, but after ¼+¼, Emily comes on, but ¼+¼ is really 1/2, so when Emily starts, is really half-way through, or the midpoint of that distance.
Emily's turn ends ¼ of the way later, which will be pretty much half-way in between (1, -½) and (-6, -7), so is really the midpoint of those two.