$(document).ready(function () {
    $("div#home .divisions > ul > li").each(function () {
        showRandomImage(this);
    });

    $(".divisions > ul").cycle({
        fx: 'fade',
        after: showRandomImage
    });

    function showRandomImage(element) {
        var images = $("img", element);
        images.hide();

        var randomIndex = Math.floor(Math.random() * images.length);
        $(images[randomIndex]).show();
    }
});