list all xcode versions installed on MAC

I'm assuming you're new to Mac - if you're not and I'm telling you stuff you already know, apologies. If you right-click on an Xcode project file and select 'Open in' ('open with'? can't remember) then you'll see everything that can open that file, which should contain any Xcode versions on there (maybe not really old ones) along with other text editors and suchlike. To set a default version, right click an Xcode project and click 'get info'. From there you can select the program that will open this particular project, and there's a button to set this as the default for every file of the same type - i.e. all of your Xcode projects.

I am New to Mac.Thanks for the detailed instructions.

I did Open with and I see Xcode 7.3

I did right click and I see Xcode (default) (7.3)

When Project is open, I have a Project Document-> Project Format ( which has )

Xcode 6.3-compatible

Xcode 3.2-compatible

Xcode 3.1-compatible

I was thinking I have Xcode 3.1, 3.2, and 6.3 installed on my computer.

I am thinking I only have Xcode 7.3 installed on my Mac.

While the Xcode 3.1, 3.2, and 6.3 are just for backward compatible option.

Is that correct?

Yes, you're correct. Those options are just for choosing the project file format used by Xcode. It does not tell you anything about what version(s) of Xcode you have. To find out if you have any extra versions of Xcode hiding on your Mac, Simpsonics's advice is good, but I recommend using the Developer pane of System Information or doing a Finder search for "Xcode" or "Xcode-beta."