For a segment of a radio show, a disc jockey can play 6 records. If there are 11 records to select from, in how many ways can the program for this segment be arranged?
This problem is asking for the number of ways to arrange 6 out of 11 records.
This can be calculated using the combination formula:
C(n, r) = n! / (r!(n-r)!)
Where n = 11 (total number of records) and r = 6 (number of records to be selected)
C(11, 6) = 11! / (6!(11-6)!)
C(11, 6) = 462
Therefore, there are 462 ways to arrange the program for this segment.