PAKI SAGOT PO THANKS. 7. A statue is to be placed on each corner of a hexagonal platform in your city park. In how many ways can these statue be placed if two of the six statues should stand next to each other?
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First, we can arrange the six statues without any restrictions. The number of ways to do this is 6! = 720.
Next, we need to consider the restriction that two of the statues must stand next to each other. We can treat these two statues as a single unit, so there are now five units to arrange. The number of ways to arrange the five units is 5! = 120.
However, we need to consider that the two statues can be arranged in two ways (either the first statue is next to the second, or the second statue is next to the first). Therefore, we need to multiply the number of ways to arrange the five units by 2.
So the total number of ways to place the statues with two of them standing next to each other is 2 x 5! = 240.
Therefore, there are 240 ways to place the statues if two of the six statues should stand next to each other.