The answer is: typically 80 days in total.
Here's the details:
1. If a domain name is expired and there's no response from the domain name owner, the domain registrar will typically send out a delete command after 45 days, to remove the domain name out from the registry.
If the domain name was registered at Godaddy.com, this period will be 42 days. Here is a detail explanation on Godaddy website.
2. There's a 30-day Deleted Name Redemption Grace Period (RGP) required by ICANN.
3. The registry will hold the domain name for 5 days for deletion.
So, start from the expiry day, it will typically take 45+30+5= 80 days for the domain name to be available again to the public for registration.