To solve the problem of how many sets of 6 numbers can be derived from the list of provided numbers (10, 17, 18, 19, 20, 21, 23, 26, 28, 29, 30, 33, 35), we will use the formula for combinations. The formula for combinations is given by:
\[
C(n, k) = \frac{n!}{k!(n-k)!}
\]
where \( n \) is the total number of items to choose from, \( k \) is the number of items to choose, and \( ! \) denotes factorial.
In this case:
- The total number of items