There are 6 landscapes, 5 portraits, and 7 still lifes available for an art display. Two of each type of painting are selected. The paintings are each hung in one of six locations in the gallery. In how many ways could the art be displayed?
2026-03-27 03:49:02.1774583342
How many ways can multiple artworks be displayed?
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I'm assuming all the landscapes, portraits, and still lifes are unique within their own categories, correct me if I am wrong.
Multiply these together, and you get $${6\choose2} \cdot {5 \choose 2} \cdot {7 \choose 2}=15 \cdot 10 \cdot 21=3150$$There are $6$ ways to place the first painting, $5$ to place the second, etc. So the number of ways to place the paintings is $$6!=720$$Multiply the two numbers together, and you get $$3150 \cdot 720=2,268,000$$