I am provided with a value m , such that I have numbers from 1 to m ,
and another number n ( n<=m) such that I can choose any n numbers from given m numbers. Now I need to calculate number of total possible combinations such that the maximum of the selected n numbers is strictly less than the sum of remaining (n-1) numbers .
Example:- m=5 ,n=3
We have (1,2,3),(1,2,4),(1,3,4),(2,3,4),(1,2,5),(1,3,5),(2,3,5),(1,4,5),(2,4,5) and (3,4,5), out of which only (2,3,4),(2,4,5) and (3,4,5) are valid. So answer is 3.
I am not able to understand how to approach this. I have my exam tomorrow and this may be one of the questions . Please help .