Final answer:
The number of ways to arrange the digits in 9,441,111 is 42, calculated using the formula for permutations of a multiset, calculated as 7! divided by the product of the factorials of the counts of each unique digit (1! * 1! * 5!).
Step-by-step explanation:
To determine how many ways the digits in the number 9,441,111 can be arranged, we use the formula for permutations of a multiset. Since we have repeating digits, we divide the factorial of the total number of digits by the factorials of the counts of each unique digit.
The number 9,441,111 has seven digits in total. Here's the breakdown: one '9', one '4', and five '1's.
The formula for the number of permutations n! over the product of the factorials of the counts of each unique digit:
P = 7! / (1! * 1! * 5!).
Calculating this, we get: P = 7! / (1 * 1 * 120) = 5040 / 120 = 42 ways to arrange the digits of the number 9,441,111.