Final answer:
The solution to the permutation problem P(9,7) using the formula P(n, r) = n! / (n - r)! is 362,880. Hence, the correct answer is option d.
Step-by-step explanation:
An arrangement of objects in a specific order is called a permutation. Here, the components or members of sets are arranged in a linear or sequential order. The student's question relates to the use of the permutation formula to solve a problem where the number of items n is 9 and the number of positions r is 7.
The permutation formula is represented as P(n, r) = n! / (n - r)!, where '!' denotes factorial, which is the product of an integer and all the integers below it down to 1.
Using the permutation formula for P(9, 7), we calculate 9! / (9 - 7)!. This simplifies to 9! / 2!, which equals 9 x 8 x 7 x 6 x 5 x 4 x 3 / (2 x 1). The answer, therefore, is 362,880. This corresponds to option d (362,880).