How to display input options only after selecting an option from the ‘select class’ tag JQuery/JS?

Im trying to create this form page https://docs.google.com/document/d/1wu2J2Jp4KAYEVyQ6B7KSGFp_7oeDttH7DwOPLMARfws/edit . I already have a form ready for data insertion to database. I just need to stylize it so that the form changes dynamically after selection change.

<fieldset>
            <label for="#productType">Type Switcher</label>
            <select id="#productType">
                <option>--Select a Type</option>
                <option value="DVD" id="#DVD" onchange="show(this)">DVD</option>
                <option value="Book" id="#Book" onchange="show(this)">Book</option>
                <option value="Furniture" id="#Furniture" onchange="show(this)">Furniture</option>
            </select>
        </fieldset>

        <br>
        <div class="subform-test-class">
        <fieldset id="#DVD" class="info-block">
            <label for="#DVD">Size (MB)</label>
            <input type="text" id="#DVD" name="dvdSize">
                <p>*Please provide size of the DVD (MB)</p>
        </fieldset>
        <br>
        <fieldset id="#Book" class="info-block">
            <label for="#weight" id="book">Weight (KG)</label>
            <input type="text" id="#weight" name="bookWeight">
                <p>*Please provide weight of the book in KG.</p>
        </fieldset>
        <br>

        <fieldset id="#Furniture" class="info-block">
            <label for="#height" id="height">Height</label>
            <input type="text" id="#height" name="fHeight">

            <label for="#width" id="width">Width</label>
            <input type="text" id="#width" name="fWidth">

            <label for="#length" id="length">Length</label>
            <input type="text" id="#length" name="fLength">
                <p>*Please provide size of the furniture in dimensions of HxWxL</p>
        </fieldset>
    </div>
    </form>

Im trying to create it dynamic so that when you select something else, the previous fieldset changes to new one and the last selection disappears. Nothing works with my code. I tried traditional JS – same results. I already put the div as display:none in CSS. Maybe my syntax is wrong?

$('body').on('change','##productType', function(){
    if($(this).val()=="DVD")
        $("#DVD").show();
    else
        $("#DVD").hide(); 
});