How many $6-$digit numbers can be formed from the digits $0,1,3,5,7$ and $9$ which are divisible by $10$ and no digit is repeated?

If the number is to be divisible by $10,$ then unit place must be $0.$

We are provided with $6$ digits $0,1,3,5,7$ and $9$ and since we have to form a $6$ digit number with no digit repeated, we will have to use all the digits.

Since, unit place digit is $0$ and its position is fixed, the remaining number of digits can be arranged in $5!$ ways.

Therefore, required number of digits $=5!=120$