How many combinations can you make with AABbCc?

Answer 1

To find the number of unique combinations of the letters in "AABbCc", we use the formula for permutations of a multiset:

[ \frac{n!}{n_1! \times n_2! \times n_3! \times \ldots} ]

Here, (n) is the total number of letters (6), and (n_1, n_2, \ldots) are the frequencies of each unique letter. We have 2 A's, 1 B, 1 C, and 2 lowercase letters (b and c). Thus, the calculation is:

[ \frac{6!}{2! \times 1! \times 1! \times 2!} = \frac{720}{4} = 180 ]

So, there are 180 unique combinations.