In this problem :

How many unique lists of 3 numbers exist, where each number is

- 1 to 10, inclusive
- Median of the list is 5
- There is a unique mode in the list

My doubt is : In greg’s solution the pairs (5,1,5), (5,2,5) etc; are included. However, In order to calculate median, we need to arrange the no’s in ascending order. Hence. in the solution (5,1,5), (5,2,5) etc; cannot be included right? Because, if, in this case we arrange them in ascending order, we get 1,5,5, 2,5,5 which are already included in the list.

Hence the possible pairs should be :

1,5,5

2,5,5

3,5,5

4,5,5

5,5,5

5,5,6

5,5,7

5,5,8

5,5,9

5,5,10

It would be great if someone could clear this up