Question 856885
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The smallest sum the three can have is 6; 1+2+3 = 6.

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There is only 1 way the sum can be 6, that is 1+2+3=6
There is only 1 way the sum can be 7, that is 1+2+4=7
There are 2 ways the sum can be 8, they are 1+2+5=8 and 1+3+4=8
There are 3 ways the sum can be 9, they are 1+2+6=9, 1+3+5=9, and 2+3+4=9

That's 7 successful ways of getting a sum of 9 or less.

The total number of ways  of getting any sum is C(10,3) = 120 ways.

Probability of a successful sum = {{{7/120}}}, 

(which, incidentally is less than 6% of the time.) 

Edwin</pre>