SOLUTION: How many ways can the value 13 be expressed as the sum of exactly 3 different positive integers? For example, 13 = 1 + 4 + 8 is one such way. Note that 13 = 4 + 8 + 1 does not coun

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Question 288999: How many ways can the value 13 be expressed as the sum of exactly 3 different positive integers? For example, 13 = 1 + 4 + 8 is one such way. Note that 13 = 4 + 8 + 1 does not count as a “different” way since the same integers are involved in the sum.
(A) 5 (B) 6 (C) 7 (D) 8 (E) 14
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
Here are all of the possibilities:

13 = 1 + 2 + 10
13 = 1 + 3 + 9
13 = 1 + 4 + 8
13 = 1 + 5 + 7
13 = 2 + 3 + 8
13 = 2 + 4 + 7
13 = 2 + 5 + 6
13 = 3 + 4 + 6


So there are 8 different ways to express 13 as a sum of 3 distinct positive integers.