Question

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

Answer 1

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

Answer 2

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

Answer 3

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->\[\frac{ 5! }{ 2! \times 2! }\]