Could random unique selection using while cause an infinite loop?

I recently came across code that looked something like this (generates 4 random numbers in an array, this is not the actual code, I just wrote this up now, so it's untested):

var uniqueNumbers = new Array();
var count = 4;
var max = 10;

function main() {
    for (var i = 0; i < count; i++) {

        do {
            var tempNum = Math.floor(Math.random() * max); //number 0-9
        } while (arrayContains(uniqueNumbers, tempNum)) 

        uniqueNumbers.push(tempNum);
    }
}

function arrayContains(a, val) {
    for (var i = 0; i < a.length; i++) {
        if (a[i] == val) return true;
    }
    return false;
}

Is it possible that the while loop could possibly be infinite (or at least take a lot of time)? In the way that it just so happens that we continuously randomly choose a number that happens to be in the array? I imagine the probability of this happening would go up as count increases. It's kind of reminding me of bogosort.

I would think that this would be improved by selecting from a diminishing 'pool' of numbers, instead of selecting randomly, something like:

var uniqueNumbers = new Array();
var count = 4;
var max = 10;
var pool = new Array();

function main() {
    createPool();
    for (var i = 0; i < count; i++) {
        if (var tempNum = selectFromPool()) {
            uniqueNumbers.push(tempNum);
        }
    }
}

function createPool() {
    for (var i = 0; i < max; i++) {
        pool.push(i);
    }
}

function selectFromPool() {
    if (pool.length <= 0) return false;

    var selectedIndex = Math.floor(Math.random() * pool.length);
    var selectedValue = pool[selectedIndex];

    pool = pool.slice(selectedIndex, selectedIndex+1);

    return selectedValue;
}

Is this a better, less fragile way of doing it? Or is there some proof that the while loop will never be infinite because of the pseudo-random nature of computer generated random numbers?

Your first attempt is indeed in danger of getting into an infinite loop if a certain value never gets returned from rand (but any half decent PRNG will return all of them eventually).

Your second attempt is very close to the (most optimal) Fisher-Yates shuffle, with the difference that you use a separate array to store the shuffled result while shrinking the original pool.

StackExchange Code Review Q#39970, answer score: 2