How to define that participants can select only one event from an event group

How can I define that participants can select only one item within an event / item group?

If you want to limit the selection of certain events / items to exactly one within an event / item group, please first create an event / item group and then assign the events / items to that group.

We have compiled a manual on how to set up the participant registration form where you can find more details:
Configuration of the Participant Registration Module

Please go to:
Overview => Settings => Manage Event/Item Groups

• Either set the option "Selection Mode" to "Exclusive: Use radio buttons so that only one item of this group can be selected" (see image), then only one of the items can be chosen by participants as the form uses radio buttons for all events / items of this group.
• Or set the option "Selection Mode" to "Normal: All events / items of this group are independent" and for the option "Maximum Number of Items to Select from This Group" set an upper limit of 1 (see image).
  With these settings checkboxes are used and participants are allowed to de-select the events / items of this group.
  

You will find more information on how to use event groups for different selection modes here:
Overview of the Options and Selection Modes for "Event/Item Groups" and "Events/Items"