Final answer:
There are 181,440 different ways for a disc jockey to select and arrange 7 records from a total of 9 for a radio show segment.
Step-by-step explanation:
The question involves calculating the number of ways 7 records can be selected and arranged from a total of 9 available records. This is a permutation problem because the order in which the records are played matters. To solve this, we use the formula for permutations without repetition, which is P(n,r) = n! / (n-r)!, where n is the total number of items to choose from, and r is the number of items to arrange.
In this case, n=9 and r=7, so we calculate the permutation as:
P(9,7) = 9! / (9-7)! = 9! / 2! = 362,880 / 2 = 181,440.
Therefore, the disc jockey can arrange the program for this segment in 181,440 different ways.