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How many integers can be expressed as a sum of three distinct numbers chosen from the set {4, 7,10,13, ..., 46}?

 Jun 9, 2020
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If I understand your question, then you have a set consisting of 15 terms of an arithmetic sequence:

 

[46 - 4] / 3 + 1 =15 terms in your set.

To choose 3 distinct number from the set:

You have: 15C3 =455 ways of summing up 3 distinct numbers from your set of 15 numbers.

 Jun 9, 2020

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