Efficiently choosing x *different* elements in a list at random

I have a list:

a = [1,2,1,1,3,5,6,2]

I want to select, say 3 elements at random from this list, but they must all be different.

I need to preserve the 'weight' of each element, so sampling from set(a) is not possible.

So far, my solution is:

while condition == False:
    mysample = random.sample(a, 3)
    if len(set(mysample)) - len(mysample) !=0:
        condition = False
    else:
        condition = True

But this forces me to re-sample as many times as it takes for the elements to all be different. This works fine for small sampling, but for large sampling, my code becomes very inefficient...

Any ideas?

Thanks