A conference hall has 24 overhead lights. Pairs of lights are operated by switches next to the

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A conference hall has 24 overhead lights. Pairs of lights are operated by switches next to the main entrance, and each switch has three numbered settings: 0 (off), 1 (dim), 2 (bright). Find the number of possible lighting arrangements in the hall if: 

a. There are no restrictions

b. Two particular pairs of lights must be on setting 2 

c. Three lights that are not operated by the same switch and five pairs of lights that are operated by the same switch are not working.

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