To answer the question about the number of different orders in which 15 basketball players can be listed, we need to consider the concept of permutations in mathematics. A permutation is an arrangement of all members of a set into a particular sequence or order.
Given that there are 15 basketball players, we are asked to find the number of different ways we can arrange these 15 players. This is calculated by finding the factorial of 15, denoted as 15!.
The factorial of a non-negative integer [tex]\( n \)[/tex] is the product of all positive integers less than or equal to [tex]\( n \)[/tex]. Mathematically, it is represented as:
[tex]\[ n! = n \times (n - 1) \times (n - 2) \times \cdots \times 3 \times 2 \times 1 \][/tex]
For [tex]\( n = 15 \)[/tex], this would be:
[tex]\[ 15! = 15 \times 14 \times 13 \times 12 \times 11 \times 10 \times 9 \times 8 \times 7 \times 6 \times 5 \times 4 \times 3 \times 2 \times 1 \][/tex]
When you compute this product, the result is:
[tex]\[ 15! = 1,307,674,368,000 \][/tex]
Therefore, the number of different orders in which the 15 basketball players can be listed is:
1,307,674,368,000
So, the correct option is:
1,307,674,368,000
