JSFiddle - React, Tailwind, and code Playground

HTML

<input type="radio" name="1" class="radio" id="radio-001" value="001" >
<input type="radio" name="1" class="radio" id="radio-002" value="002" >
<input type="radio" name="1" class="radio" id="radio-003" value="003" >
<input type="radio" name="2" class="radio" id="radio-004" value="004" >
<input type="radio" name="2" class="radio" id="radio-005" value="005" >
<input type="radio" name="2" class="radio" id="radio-006" value="006" >
<input type="radio" name="3" class="radio" id="radio-007" value="007" >
<input type="radio" name="3" class="radio" id="radio-008" value="008" >
<input type="radio" name="3" class="radio" id="radio-009" value="009" >

<img src="" width="400px" id="image" alt="">

JavaScript

var images = {
	"001004007" : "http://hronika.info/uploads/posts/2016-01/1452736497_yumor12.jpg",
	"001004008" : "http://www.nokiaplanet.com/uploads/posts/2015-07/1436517961_cherry-drop-240x320.jpg",
	"003006009" : "http://s00.yaplakal.com/pics/pics_original/9/2/3/8037329.jpg"
};

var inp = document.querySelectorAll('input[id^="radio-"]');

for (var i = 0; i < inp.length; i++) {
	inp[i].onchange = onChange;
}

function setDefaultImage() {
		document.getElementById('image').src = "http://coe.almau.edu.kz/img/no_image.png";
}

function onChange() {
    var inputs = document.querySelectorAll('input[id^="radio-"]:checked');

    if (inputs.length == 3) {
        var str = "";
        
        for (var i = 0; i < inputs.length; i++) {
            str += inputs[i].value;
        }
        
        if (images[str] != undefined) {
            document.getElementById('image').src = images[str];
        } else {
        		setDefaultImage();
        }
		} else {
				setDefaultImage();
    }
}

setDefaultImage();