How can I count the number of radio boxes selected and validate?
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So here's what my code does: 

it displays 10 sets of radio buttons, each with 2 options. (so 20 radio buttons total). The 10 sets all have different names, but are within the same form. A person can only choose 5 buttons out of the 10. I have a piece of code that disables the radio buttons once 5 are selected. Now I want to prevent people from submitting the form if 4 or less buttons are selected. 

Here is an example of the code:

HTML:

     <form method="post" action="index.php" name="buttons" onsubmit="return Validation()">
     <input type="radio" id="button" value="first_button" name="1" />
     <input type="radio" id="button" value="second_button" name="1" />
     <input type="radio" id="button" value="first_button" name="2" />
     <input type="radio" id="button" value="second_button" name="2" />
     <input type="radio" id="button" value="first_button" name="3" />
     <input type="radio" id="button" value="second_button" name="3" />
     <input type="radio" id="button" value="first_button" name="4" />
     <input type="radio" id="button" value="second_button" name="4" />
     <input type="radio" id="button" value="first_button" name="5" />
     <input type="radio" id="button" value="second_button" name="5" />
     <input type="radio" id="button" value="first_button" name="6" />
     <input type="radio" id="button" value="second_button" name="6" />
     <input type="radio" id="button" value="first_button" name="7" />
     <input type="radio" id="button" value="second_button" name="7" />
     <input type="radio" id="button" value="first_button" name="8" />
     <input type="radio" id="button" value="second_button" name="9" />
     <input type="radio" id="button" value="first_button" name="9" />
     <input type="radio" id="button" value="second_button" name="9" />
     <input type="radio" id="button" value="first_button" name="10" />
     <input type="radio" id="button" value="second_button" name="10" />
     </form>

JAVASCRIPT


     function Validation()
     {
     var bol=document.getElementById("button").value
     var bol2=(bol.length);
     if (bol2<=4)
       {
       alert("Please select 5 buttons");
       return false;
       }
     }

I already know my java code does not work because the .length code is counting the number of characters and not the value. I would like it if someone could help me figure out how to count the number of radio buttons checked. 

Thanks