I must let new customers to input their preferred password within the same registration form when they're signing up on my small Wordpress site.

You may already know automatically the registration form only asks the brand new user to go in username and email, next the machine will email the consumer having a produced password. However I dont need it, this isn't appropriate for this site because it does not have mail function working(it is a free hosting service).

Thanks greatly for your kind help. Any assistance is greatly appreciated!

*It's ok basically must edit the core files of wordpress, thanks! Please kindly guide me.

This wordpress plugin allows your customers to produce their very own passwords when signing up for the site http://wordpress.org/extend/plugins/theme-my-login/