Question

How many different six-digit numbers are there whose three digits are even and three digits are odd?

Answer 1

From $6$ digits: $3$ odds and $3$ even

$\Rightarrow$ $1^{st}$ digit be even $:$ $4\ast 4\ast 3\ast 5\ast 4\ast 3\ast 5!$

$1^{st}$ digit be odd$:$ $5\ast 4\ast 3\ast 5\ast 4\ast 3\ast 5!$$=120\ast (64\ast 9\ast 5+3600)=120\ast (2880+3600)=77760$ ways$.$