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Damien Bosco

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The total combination without restriction is 32 (2x2x2x2x2). If zero is off and 1 is on it can be represented like this,

00000, 00001, 00010, 00011, 00100, 00101, 00110, 00111, 01000, 01001, 01010, 01011, 01100, 01101, 01110, 01111, 10000, 10001, 10010, 10011, 10100, 10101, 10110, 10111, 11000, 11001, 11010, 11011,11100, 11101, 11110, 11111

as no zero can be next to another there are 13 combinations.

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Q: In how many different ways can a panel of five on-off switches be set if no two adjacent switches can be off?
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