Final answer:
The number 7,555,111 can be arranged in 840 different ways.
Step-by-step explanation:
The number 7,555,111 contains 7 digits.
To find the number of ways the digits can be arranged, we can use the concept of permutations.
Since the number contains repetitive digits, we need to consider that the arrangements with the same digits in different positions are considered to be the same arrangement.
The number of ways the digits can be arranged is calculated using the formula:
p = n! / (n1! imes n2! imes ... imes nk!)
where p is the number of permutations, n is the total number of digits, and n1, n2, nk are the frequencies of each digit.
In this case, there are 7 digits in total, with 3 fives, 2 ones, and 1 seven.
Therefore, the number of ways to arrange the digits is:
p = 7! / (3! imes 2! imes 1!) = 7 imes 6 imes 5 imes 4 = 840.