You can install Office, Project, and Visio on the same computer. But, there are some combinations of Office, Project, and Visio that can't be installed together on the same computer.
The two main things that determine whether Office, Project, and Visio can be installed together on the same computer are the version of the product and the installation technology used to install the product. What governs whether an installation scenario is supported are these two rules:
- You can't install two products together that have the same version but use different installation technologies.
- You can't install two products of different versions together if both products use Click-to-Run as the installation technology and those products have overlapping Office applications.
You can get the information from this link: https://learn.microsoft.com/en-us/deployoffice/install-different-office-visio-and-project-versions-on-the-same-computer
For Office 2016, have a version of 16.0 and used Click-to-Run (C2R) as the installation technology.
For Office 2010, had a version of 14.0 and used Windows Installer (MSI) as the installation technology.
So you can install Office 2016 and Project 2010 in the same computer.
Hope the information is helpful.
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