For a segment of a radio show, a disc jockey can play 8 records. If there are 11 records to select from, in how many ways can the program for this segment be arranged?

Step 1 ：This problem is about permutations. A permutation is an arrangement of objects in a specific order. The order of arrangement of the object is very important. The number of permutations of 'n' items taken 'r' at a time, is determined by the formula: \(P(n, r) = n! / (n-r)!\)

Step 2 ：In this problem, a disc jockey can play 8 records in a segment of a radio show. There are 11 records to select from. So, we need to find the number of permutations of 11 items taken 8 at a time.

Step 3 ：Substitute n=11 and r=8 into the formula: \(P(11, 8) = 11! / (11-8)!\)

Step 4 ：Calculate the factorial of 11 and 3: \(11! = 11 \times 10 \times 9 \times 8 \times 7 \times 6 \times 5 \times 4 \times 3 \times 2 \times 1 = 39916800\) and \(3! = 3 \times 2 \times 1 = 6\)

Step 5 ：Substitute the factorial values into the formula: \(P(11, 8) = 39916800 / 6 = 6652800\)

Step 6 ：So, the total number of ways to arrange the program is \(\boxed{6652800}\)