Final answer:
There are 362,880 ways to arrange the digits in the number 9,164,461.
Step-by-step explanation:
To find the number of ways the digits in the number 9,164,461 can be arranged, we can use the concept of permutation. Since the number consists of 9 digits, we have 9 positions to fill. The first position can be filled with any of the 9 digits, the second position can be filled with any of the remaining 8 digits, and so on.
Therefore, the total number of ways the digits can be arranged is 9 × 8 × 7 × 6 × 5 × 4 × 3 × 2 × 1, which is the same as 9 factorial (9!). Using a calculator, we can find that 9! is equal to 362,880. So, there are 362,880 ways to arrange the digits in the number 9,164,461.