How many ways can the digits in 9633333 be arranged?

Answer 1

To find the number of ways to arrange the digits in 9633333, we first note that there are 7 digits total, with the digit '3' appearing 4 times. The formula for permutations of a multiset is given by:

[ \frac{n!}{n_1! \cdot n_2! \cdot \ldots \cdot n_k!} ]

Here, (n = 7) (total digits), and the counts for each distinct digit are: '9' (1), '6' (1), and '3' (4). Thus, the calculation becomes:

[ \frac{7!}{1! \cdot 1! \cdot 4!} = \frac{5040}{24} = 210 ]

Therefore, there are 210 unique arrangements of the digits in 9633333.