Final answer:
The digits in the number 7,553,333 can be arranged in 42 different ways, calculated by dividing the factorial of the total number of digits by the factorial of the count of each repeated digit.
Step-by-step explanation:
To determine how many ways the digits in the number 7,553,333 can be arranged, we use the formula for permutations of a multiset. The number has 7 digits with the following counts: one 7, one 5, and five 3s. The general permutation formula is n! divided by the factorial of each uniquely repeated digit's count. Hence, the calculation will be the factorial of 7 (7!) divided by the factorial of the count of 3s (5!).The number 7,553,333 has 8 digits. To find the number of ways the digits can be arranged, we can use the concept of permutations. Since all the digits are different, we can use the formula for permutations of distinct objects:
n!
Thus, the number of arrangements is 7! / 5! = (7×6×5×4×3×2×1) / (5×4×3×2×1) which simplifies to 7×6 / 1 = 42 arrangements. Therefore, there are 42 different ways to arrange the digits in the number 7,553,333.