A set S is composed of 20 multi-colored objects

[Mr Greene]

The scenario specifies 3 blue objects are picked.

Nope. The scenario specifies four are picked. but only the most suitable are selected.

If the fourth can be any colour including blue

As specified, it matters not what the fourth colour is.

then no matter what position the 'any-colour' object is picked the chances are 20/20, 19/19, 18,18 or 17/17. in any case the the answer is 1 and multiplying that by the chances for the blue selections would be a pointless exercise.

False. Actually obviously false. Only 12 out of twenty can be "not-blue". To claim 50/50 and then claim claim that all objects are blue or red is nonsense, which immediately torpedoes you argument. You are flying at that point, in the face of one's own argument.

The extra selection must therefore be 'not-blue' if the scenario has any purpose.

Nope. They decision of blue or not blue is arbitrary. Arbitrary decisions have no purpose by definition.

This would insert a (12/X) selection into the matrix with four permutations.

12x? I would dearly like to consider that a typo. I hope so, but I fear not.

It seems similarly pointless if the object is returned to the pool before next draw.

Rather meaningless. Nobody gets "returned" to anything. There is no evidence of anyone being returned to anything. Why would any rational person accept anyone accept anything about a person being returned from anything to anywhere?

And bear in mind that I am an OOBE witness, an NDE witness, through personal experience, so please do not wheel out the usual baloney.

Is English not your first language?
4 selections from 20, 3 of which are blue, the 4th has to be non-blue or the probability is 1 rendering the exercise pointless as there's no point multiplying by 1.

[Fireball]

I have a probability question that I need to solve:

A set S is composed of 20 multi-colored objects. 4 objects were chosen randomly from S.
What is the probability that 3 of the chosen objects be blue; knowing that there are 8 blue objects in S ?

Zero. The question clearly states that "A set S is composed of 20 multi-colored objects." None of them are blue, so it doesn't matter how many of them you pick.

Better question: If you try and get the internet to do your homework for you what are the odds that one of the replies is actually your mom's phone number?

867-5309