How many different six digited numbers can be written using 504477?

Question

imqwerty · Answer

$$\frac{ 6! }{ 2! \times 2! }-\frac{ 5! }{ 2! \times 2! }$$
$$\frac{ 6!-5! }{ 2! \times 2! }$$$$\frac{ 600 }{ 4}=150$$

anonymous · Answer

why did we use 5! is it because there is 0?

imqwerty · Answer

yes
$$\frac{ 6! }{ 2! \times 2! }$$ represents all the different possible numbers that can be formed from the given digits. 
but it also includes number which have 0 at the starting and we need to remove those numbers.

all diff numbers starting with 0->$$\frac{ 5! }{ 2! \times 2! }$$