SOLUTION: Five cards are drawn at random from an ordinary deck of 52 cards. In how many ways is it possible to draw two red aces and two black jacks? Answer is 48, but why?

48 is wrong.

The answer is 1 way if it doesn't matter what order you draw those four 
cards in, and 24 ways if you are counting how many different orders 
that you could draw them in.

That's because:

There are ONLY TWO red aces, the ace of hearts 
and the ace of diamonds.
 
Also, there are ONLY TWO black jacks, the jack of spades 
and the jack of clubs.

So there is only 1 way to draw those 4 cards and that
1 way is simply to draw them!

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Now if you are drawing them one by one, and you are counting
how many different orders in which you can draw them, then

1.  There are 4 ways to draw the 1st of those 4 cards.
2.  For each of those 4 ways you could draw one of those 4 cards,
    you can draw any of the remaining 3 cards 3 ways.
    That's 4×3 or 12 ways to draw the first two of those cards.
3.  For each of those 4×3 or 12 ways you could have drawn the first two
    of those cards, you can draw any of the remaining 2 cards  ways.
    That's 4×3×2 or 24 ways to draw the first three of those cards.
4.  There is only 1 way to draw that remaing card. 

So the number of different orders in which you could have drawn those 
four cards is 4×3×2×1 = 4! = 24 ways.

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So there is just 1 way to draw the four cards, and that one way is to
draw them!

If you are drawing them in a certain order, then there are 24 different
orders in which you could draw them.

But the answer is certainly not 48.  It's either 1 or 24.

Edwin