How many different numbers of six digits can be formed from the digits $2, \; 3, \; 0, \; 7, \; 9, \; 5$ when repetition of digits is not allowed?
The given digits are $2, \; 3, \; 0, \; 7, \; 9, \; 5$
$\because$ $\;$ The lakh's place cannot be a $0$, it can be selected from the given digits in $5$ ways.
Now, the ten-thousand's place can be selected from the remaining 5 digits (since repetition of digits is not allowed) in $5$ ways.
The thousand's place can be selected from the remaining 4 digits in $4$ ways.
The hundred's place can be selected from the remaining 3 digits in $3$ ways.
The ten's place can be selected from the remaining 2 digits in $2$ ways.
The unit's place can be selected from the remaining 1 digit in $1$ ways.
$\therefore$ $\;$ Total number of ways of forming a six digit number using the given digits (without repetition) is $5 \times 5 \times 4 \times 3 \times 2 \times 1 = 600$ ways