Final answer:
The question is about calculating permutations, a mathematical concept used to determine the number of ways the first six songs on a playlist can be arranged when choosing from a total of 20 songs.
Step-by-step explanation:
The student is asking about the number of different ways a DJ can arrange the first six songs on a playlist, given a total of 20 songs to choose from. This is a problem of permutations in mathematics.
To find the number of different arrangements for the first six songs, we use the formula for permutations, which is P(n, k) = n! / (n-k)!, where n is the total number of items, and k is the number of items to arrange. In this case, n is 20 and k is 6. Therefore, the calculation is as follows:
P(20, 6) = 20! / (20-6)! = 20! / 14! = 20 × 19 × 18 × 17 × 16 × 15
This calculation will give us the total number of possible arrangements for the first six songs on the DJ's playlist, illustrating the concept of permutations within the subject of combinatorics.