You can
put this solution on YOUR website! .
The number of ways to select one or more students from 6 students is equal to the number of non-empty subsets in the set of 6 students.
It is very well known fact that the set of N elements has 
subsets, including an/the empty subset and the improper subset.
In your case, N = 6 and the emty subset is excluded, so the number under the question is 
= 64-1 = 63.
Solved.
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For discussion and the proof of this fact see the lesson
- How many subsets are there in a given finite set of n elements?
in this site.
