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The correct answer is 10*9/2 = 45. The 45 are:

01, 02, 03, 04, 05, 06, 07, 08, 09

12, 13, 14, 15, 16, 17, 18, 19,

23, 24, 25, 26, 27, 28, 29,

34, 35, 36, 37, 38, 39,

45, 46, 47, 48, 49,

56, 57, 58, 59,

67, 68, 69

78, 79,

89.

In a combination, the order of the elements DOES NOT MATTER.

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