Change ListBox.ItemsSource Binding property on Button.Click?

Quick question...

I have a ListBox with its ItemsSource property bound to a collection property in a viewmodel like so:

<ListBox Name="CollectionsListBox" ItemsSource="{Binding Activity.Timesheets}" />

I also have two Button objects in the same view. The question is... can I change the CollectionsListBox ItemsSource Binding from Activity.Timesheets to Activity.Attachments using just XAML?

Failing that, from the viewmodel using Command objects?

EDIT >>>

I found a simple solution by using RadioButtons instead of Buttons from part of Howard's answer:

<ListBox Name="CollectionsListBox">
    <ListBox.Style>
        <Style>
            <Style.Triggers>
                <DataTrigger Binding="{Binding ElementName=TimesheetsButton,Path=IsChecked}" Value="True">
                    <Setter Property="ListBox.ItemsSource" Value="{Binding Activity.Timesheets}" />
                    <Setter Property="ListBox.ItemContainerStyle" Value="{StaticResource TimesheetStyle}" />
                </DataTrigger>
                <DataTrigger Binding="{Binding ElementName=AttachmentsButton,Path=IsChecked}" Value="True">
                    <Setter Property="ListBox.ItemsSource" Value="{Binding Activity.Attachments}" />
                    <Setter Property="ListBox.ItemContainerStyle" Value="{StaticResource AttachmentStyle}" />
                </DataTrigger>
            </Style.Triggers>
        </Style>
    </ListBox.Style>
</ListBox>

Many thanks for the help.