how to create dropdownlist with checkbox and after client selected the values, the total count of selected items will replace the text area in dropdownlist

What do you mean "total count will replace..." - will your dropdownlist simply show a number (i.e. 5 for five selected items)? What are you trying to do?

Dropdownlist with checkboxes: there are several examples, one of them here on CP (that I know of) - or use checkboxlist if you have small number of items...or use collapsible panel with repeater that contains checkbox in its itemTemplate...there are plenty of solutions, just do some research.