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Question 13

Triples of odd numbers $$\left(a,b,c\right)$$ with $$a<b<c$$, with $$a,b,c$$ from $$1$$ to $$10$$ are generated such that $$a+b+c$$ is prime number. The number of such triple is

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The odd numbers available are $$1,3,5,7,9$$. The triples whose sums are prime are $$\left(1,3,7\right)$$, $$\left(1,3,9\right)$$, $$\left(1,5,7\right)$$, $$\left(1,7,9\right)$$, $$\left(3,5,9\right)$$ and $$\left(3,7,9\right)$$. Hence there are $$6$$ such triples.

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