I recommend creating an Enum for these options:
public enum MyOptions
{
Option1,
Option2,
Option3
}
Then create a property in the ViewModel which holds a value from this Enum:
public class MyViewModel
{
public MyOptions SelectedOption {get;set;} //NotifyPropertyChange() is required.
}
Then bind these RadioButtons
using the EnumToBoolConverter
<RadioButton IsChecked="{Binding SelectedOption, Converter={StaticResource EnumToBoolConverter}, ConverterParameter=Option1}"/>
<RadioButton IsChecked="{Binding SelectedOption, Converter={StaticResource EnumToBoolConverter}, ConverterParameter=Option2}"/>
<RadioButton IsChecked="{Binding SelectedOption, Converter={StaticResource EnumToBoolConverter}, ConverterParameter=Option3}"/>
Then, you determine which option is selected by a simple switch
in the ViewModel:
public void SomeMethod()
{
switch (SelectedOption)
{
case MyOptions.Option1:
...
case MyOptions.Option2:
...
case MyOptions.Option3:
...
}
}