prolk,
<!DOCTYPE html>
<html>
<head>
<title>Untitled</title>
<meta charset="utf-8">
</head>
<body>
<form name="form">
<input type="checkbox" name="var" value="var1"> <span>VARIANT 1</span><br>
<input type="checkbox" name="var" value="var2"> <span>VARIANT 2</span><br>
<input type="checkbox" name="var" value="var3"> <span>VARIANT 3</span><br>
<input type="checkbox" name="var" value="var4"> <span>VARIANT 4</span><br>
<input type="checkbox" name="var" value="var5"> <span>VARIANT 5</span><br>
<input type="button" value="next" disabled="disabled">
</form>
<script>
document.addEventListener("DOMContentLoaded", function() {
var btn = document.querySelector('[type="button"]');
document.querySelector('[name="form"]').addEventListener("click", function(event) {
var target = event.target;
if (target.name == "var") {
var check = document.querySelectorAll('[name="var"]:checked');
check.length < 3 ?
btn.setAttribute("disabled", "disabled") :
btn.removeAttribute("disabled")
}
})
});
</script>
</body>
</html>