Need help with this other problem

[Nicolita]

Given:
A standard deck of playing cards contains total of 52 cards(26 red cards and 26 black cards). There are 4 cards of each number 2 through 10 (two red and two black). There are 12 face cards (four jacks, four queens, and four kings) and four aces.

Task C: Separate the 12 face cards from the rest of the deck. Assume that the remaining cards have been shuffled. Select Three cards from the pile of face cards. For each question, show how you derive the solution.

How may ways are there of selecting one of each face cards from the pile?

These are my answers, please let me know if I am correct.

There are 12 face cards
There are four jacks, four queens, four kings, and four aces.

Number of ways of selecting one jack from 4 jack = 4C1
Number of ways of selecting one queen from 4 queens=4C1
Number of ways of selecting one king from 4 kings=4C1

The number of ways of selecting one of each face card from the pile = 4*4*4*=64/12= 5 ways

How many ways are there of selecting the queen of clubs, then the king of diamonds, and then the
jack of hearts from the pile?

There are 12 face cards.

The number of ways of selecting the queen of clubs, then the king of diamonds, and then the jack
of hearts from the pile is

= 12 * 11 * 10 = 1320/12= 55 ways


How many ways are there of selecting three of the same crds (i.e., 3 jacks. 3queen, or 3 kings ) from the pile?

There are 12 face cards.

The number of ways of selecting three of the same face cards = 3* 3* 3 = 27/12 = 2 times.

Thank you so much for you help.

Maritza Glascock.

 

[pka]

Please note that the question is about number of ways!
So three face cards gives you (4)(4)(4)=64 ways.

If we count an ace as a face card then the answer is: <SUB>4</SUB>C<SUB>3</SUB>(4)(4)(4).

 

[Gene]

There are 12 face cards (four jacks, four queens, and four kings) and four aces.

Seems to me that you are letting formulas get in the way of logic. You know your answer is wrong. There must be an integer answer 'cause there can't be half a way. Either you can or you can't. Your 64/12 is not an integer.
Also you are changing the definition of "face cards" in your math. Above you say that aces ARE face cards.

How may ways are there of selecting one of each face cards from the pile?

Does that mean one of each rank? It doesn't really say so.
Does how many ways include the order? Is
JD, QH, KS, AD a "different way" than
QH, JD, KS, AD?
Again, it doesn't really say.
I would say the answers are yes and no respectively. If that is right you are close.
From logic you can choose any of 4 aces, kings, queens and jacks. 4*4*4*4 or (4C1)^4.

How many ways are there of selecting the queen of clubs, then the king of diamonds, and then the jack of hearts from the pile?

There is only one way of selecting the queen of clubs. Ditto the other two.
1*1*1=1
This one does give the order.

How many ways are there of selecting three of the same crds (i.e., 3 jacks. 3queen, or 3 kings ) from the pile?

The first choice works no matter which card is picked. After that there are 3C2 ways for the next 2. So there are 12*3C2 ways of getting three of a kind.

 

[pka]

This is post script, a bit trivia for information.
For someone who lives in an area of high concentrations of casinos, I remain ignorant of most gamming rules.
So I finally got around to consulting a local expert.
According to the strict rules an ace is not a face card but is an honor card.
There are 12 face cards but 16 honor cards in a standard deck.
This illustrates the need of extra care in writing questions.

 

[Nicolita]

The solutions for 1 and 3 are incorrect.
Teacher comments:
In both question the student is beginning with all 12 cards as possible choices. As one card is chosen each time, the total possible to chose from will decrease each time. For example, if the student picks a jack the first time in the third question, then the student can no longer count any of the queens, and the kings as possible choices. Continue with through the third draw.
Thank You, so much for all you help.

 

[Denis]

Ah c'mon Nicolita: look at your original post:
you're talking WAYS TO PICK, not probabilities;
tell your teacher to make up his/her mind!

Like, the PROBABILITY of picking queen of hearts from 12 cards is 1/12...

The PROBABILITY of picking the 2 of diamonds followed by the 7 of clubs
from the full deck of 52 cards is 1/52 * 1/51.