You could do it without code behind.
You could add two states to your control: male and female.
Then you define your two states:
Male state: maleCombobox = Visible, femaleCombobox = Collapsed
Female state: : maleCombobox = Visible, femaleCombobox = Collapsed
Here is the sample xaml (just a quick sample ;) ):
<UserControl xmlns:sdk="http://schemas.microsoft.com/winfx/2006/xaml/presentation/sdk"
xmlns="http://schemas.microsoft.com/winfx/2006/xaml/presentation"
xmlns:x="http://schemas.microsoft.com/winfx/2006/xaml"
xmlns:d="http://schemas.microsoft.com/expression/blend/2008"
xmlns:mc="http://schemas.openxmlformats.org/markup-compatibility/2006"
xmlns:i="http://schemas.microsoft.com/expression/2010/interactivity" xmlns:ei="http://schemas.microsoft.com/expression/2010/interactions" x:Class="SilverlightApplication1.MainPage"
mc:Ignorable="d"
d:DesignHeight="300" d:DesignWidth="400">
<Grid x:Name="LayoutRoot" Background="White">
<VisualStateManager.VisualStateGroups>
<VisualStateGroup x:Name="MaleFemaleState">
<VisualState x:Name="FemaleState">
<Storyboard>
<ObjectAnimationUsingKeyFrames Storyboard.TargetProperty="(UIElement.Visibility)" Storyboard.TargetName="FemaleCB">
<DiscreteObjectKeyFrame KeyTime="0">
<DiscreteObjectKeyFrame.Value>
<Visibility>Visible</Visibility>
</DiscreteObjectKeyFrame.Value>
</DiscreteObjectKeyFrame>
</ObjectAnimationUsingKeyFrames>
</Storyboard>
</VisualState>
<VisualState x:Name="MaleState">
<Storyboard>
<ObjectAnimationUsingKeyFrames Storyboard.TargetProperty="(UIElement.Visibility)" Storyboard.TargetName="MaleCB">
<DiscreteObjectKeyFrame KeyTime="0">
<DiscreteObjectKeyFrame.Value>
<Visibility>Visible</Visibility>
</DiscreteObjectKeyFrame.Value>
</DiscreteObjectKeyFrame>
</ObjectAnimationUsingKeyFrames>
</Storyboard>
</VisualState>
</VisualStateGroup>
</VisualStateManager.VisualStateGroups>
<i:Interaction.Triggers>
<ei:PropertyChangedTrigger Binding="{Binding IsChecked, ElementName=MaleRB}">
<ei:GoToStateAction StateName="MaleState"/>
</ei:PropertyChangedTrigger>
<ei:PropertyChangedTrigger Binding="{Binding IsChecked, ElementName=FemaleRB}">
<ei:GoToStateAction StateName="FemaleState"/>
</ei:PropertyChangedTrigger>
</i:Interaction.Triggers>
<StackPanel>
<RadioButton GroupName="1" x:Name="MaleRB" Content="Male"/>
<RadioButton GroupName="1" x:Name="FemaleRB" Content="Female"/>
</StackPanel>
<Grid Margin="40">
<ComboBox x:Name="MaleCB" Visibility="Collapsed">
<ComboBoxItem Content="Male"/>
</ComboBox>
<ComboBox x:Name="FemaleCB" Visibility="Collapsed">
<ComboBoxItem Content="female"/>
</ComboBox>
</Grid>
</Grid>
</UserControl>
Unfortunately for the triggers you need the blend libs. If you don't have blend, you can download a trial or you can define your states and use the VisualStateManager.GoToState in your code behind (http://msdn.microsoft.com/de-de/library/system.windows.visualstatemanager.gotostate(VS.95).aspx). You would listen on the checked event of each radio button and would go to the needed state.
Hope this helps, if you need further explanation just write a comment.
TJ