How many combinations can you make with 4, 4, 7 and 7?

Question

Is there a formula you can use to calculate how many 4 digit combinations you can make using only 2 fours and 2 sevens?

Answer 1

If you are looking for a strategy applicable in more general cases: There are $4!$ different orders of these four digits, however the orders with two $4$s or $7$s interchanged are the same, so we need to divide by $2$ for each of those degeneracies, getting $4!/(2\cdot 2) = 6$