Equal distribution of letters on a 4x4 board

I am making a game, in which a user types or to be precise clicks on a 4x4 board to create a meaningful word. The issue is my random distribution of letters on the board leads to prevailing of consonants, which makes it hard to find words. Like on the picture (only 3 vowels). So my question, is there any formula or algorithm to distribute consonants and vowels nearly equally maybe 10 (consonants) to 6 (vowels)? Or can you suggest a solution.

The way I display letters randomly is the following:

    const letters = ['a','b','c','d','e','f','g','h','i','j','k','l','m','n','o','p','q','r','s','t',
 'u','v','w','x','y','z'];

    var searched_word = '';
    var tr = '';
    var wordsBank = [];
    var wordsCount = 0;

    var boxes = document.querySelectorAll('.square');
    //console.log(boxes);

    boxes.forEach(function(box) {
      box.addEventListener('click', function(e) {
        e.preventDefault();
        searched_word += this.innerHTML;
        document.querySelector('.input').value = searched_word;
      });

      console.log(searched_word);
      return searched_word;
    });

    function randomLetters(boxes) {
      for (var i = 0; i < boxes.length; i++) {
        let box = boxes[i];
        let randomLetterNumber = Math.floor(Math.random() * letters.length);
        box.innerHTML = letters[randomLetterNumber].toLocaleUpperCase();
        //console.log(box);
        //console.log(randomLetterNumber);
      }
    }