How many distinct set of three positive integers have a mean of 6, a medium of 7 no mode ?

3 sets.

1 7 10

2 7 9

3 7 8.

Step-by-step explanation:

The sum must be 18 ( 3*6)  and 7  is the middle number ( the median).

So the first and last numbers must add up to 11  with the first number less than 7.  As there is no mode no number can be repeated.

So one set is 3 7 8    (the first number can't be 4 as the last number would have to be 7)

Others are 2 7 9,

1 7 10.

step-by-step explanation:

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