var i, tmp, len = 20, pass = "";

function charGen() {
    return String.fromCharCode(Math.floor(Math.random() * (0x5a - 0x41) + 0x41));
};

function numGen() {
    return String.fromCharCode(Math.floor(Math.random() * (0x39 - 0x30) + 0x30));
};

function SymbGen() {
    return String.fromCharCode(Math.floor(Math.random() * (0x2f - 0x21) + 0x21));
};

for (i = 0; i < len; i++) {
    tmp = Math.floor(Math.random() * (5 - 1) + 1);
    switch(tmp){
        case 1:
            pass += charGen();
            break;
        case 2:
            pass += numGen();
            break;
        case 3:
            pass += SymbGen();
            break;
    };
};

<input type="checkbox" class="checkboxes" name="genMethod">
<span>Number</span><br>
<input type="checkbox" class="checkboxes" name="genMethod">
<span>Symbols</span><br>
<input type="checkbox" class="checkboxes" name="genMethod">
<span>Chars</span><br>