There are several information's already given in the question. Based on those given information's the answer to the question can be easily deduced.
Number of people in each committee = 6
Then
Number of distinct committees of 6 people = 17/[(17 - 6) * 6]
= 17/(11 * 6)
= 17!/11!6!
I hope that this is the answer that you were looking for and the answer has actually come to your desired help.