Please find attached qvw. This is the way I have done it in tha past.
You need to add an expression as 1. and go to Presentation tab and hide the column.
for bar chart, uncheck bar in display option
Adding a 1 didn't help you in your current example because your second expression was always going to be 1.
You could set your second expression to invisible, like parabgautam suggests. This will hide your Count(Desc) but still use it to display the Type label on your X-Axis.