Выделить button при нажатом tabPage c#

Нужно подписаться на событие SelectedIndexChanged:

private void tabControl1_SelectedIndexChanged(object sender, EventArgs e)
{
    switch (tabControl1.SelectedIndex)
    {
        case 0:
            button1.BackColor = Color.Red;
            button2.BackColor = button3.BackColor = button4.BackColor = Color.Empty;
            break;
        case 1:
            button2.BackColor = Color.Red;
            button1.BackColor = button3.BackColor = button4.BackColor = Color.Empty;
            break;
        case 2:
            button3.BackColor = Color.Red;
            button1.BackColor = button2.BackColor = button4.BackColor = Color.Empty;
            break;
        case 3:
            button4.BackColor = Color.Red;
            button1.BackColor = button2.BackColor = button3.BackColor = Color.Empty;
            break;
        default:
            break;
    }
}