Question

If each permutation of the digits 1,2,3,4,5,6 are listed in the increasing order of the magnitude, then 289th term will be ?

Answer 1

Suppose we pick 3 numbers x,y,z∈{1,2,3,4,5,6,7,8} and form a 3 digit number xyz how many possible combinations numbers can we create such that x<y<z. For example 357 would be one such combination.

 I'm struggling with this problem here is what I have so far, we know that x≤6 otherwise there aren't enough numbers in the list to make an increasing sequence. So we have 6 choices for the first digit. Now is where I am stuck on what to do next.