Final answer:
The number of different arrangements for the digits in the number 7,440,000 can be calculated using the permutations formula for a multiset, which is 7!/(1! * 2! * 4!).
Step-by-step explanation:
The question asks about the number of ways the digits in the number 7,440,000 can be arranged. This involves factorial expressions and permutations of non-unique items. The number 7,440,000 has one '7', two '4's, and four '0's. To calculate the different arrangements, we use the formula for permutations of a multiset:
n! / (n1! * n2! * ... * nk!), where n is the total number of items to arrange, and n1, n2, ..., nk are the frequencies of each unique item. Here, it's 7!/(1! * 2! * 4!), which gives us the total number of arrangements.