Expert: Abe Mantell - 1/3/2008

Question
This may sound similar to the last question I asked but it is not. Please take a look if you can.

Given: Separate the 12 face cards from the rest of the deck. Discard the rest of the deck. For this problem you only need the 12 face cards (4 jacks, 4 queens, 4 kings). Select 3 cards from the pile of face cards. For the following question, show how the solution has been derived.

Question:
How many ways are there of selecting one of each face card from the pile? This is where it is different. The selections is ONE OF EACH FACE CARD (the last question I posted dealt with 3 of the same face cards).

Here is what my professor has told me (after many submissions of the assignment on my part, and still not passing):

The fundamental counting principle must be used. This requires multiplying three numbers together.
Please determine the number of favorable outcomes for each draw.
How many face cards are in the deck? If a king is drawn first, then a queen or a jack must be drawn second. How many queens + jacks are in the deck for the second draw? How many cards are available for the third draw?

Can you help?

Answer
Hello again Celeste,

We want: ONE Jack, ONE Queen, and ONE King
Since there are 4 of each, there are 4*4*4=64 ways
of selecting one of each.

Another way...
First Card can be any one of the 12 cards.
Second Card can be any of the "other" 8 cards.
Third Card must be one of the 4 cards not yet chosen.
So, there are 12*8*4 permutations, but since we do not
care about the order (right?), we need to divide by 3!
(i.e. the number of ways to rearrange the 3 cards).
So, we get 12*8*4/6=64, as above.

OK?

Abe