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Jeff is choosing three numbers from the set {1, 2, 3, ..., 12}. How many ways can Jeff choose three numbers, so that no two chosen numbers are consecutive?

 Nov 13, 2021
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Example: 1 3 7

 

For the first number, you have 12 choices.

For the 2nd number, you have 10 choices [which excludes the first choice and its consecutive number]

For the 3rd number, you have only 8, choices [excluding the 1st and the 2nd and its consective number]

 

So, you have: 12  x  10  x  8 ==960 ways of picking 3 numbers out of 12.

 Nov 14, 2021
edited by Guest  Nov 14, 2021

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