Probabilty, combinations, deriviations, permutations (cards)

[agmoore]

I need help I put in my answers after the questions

1.How many different arrangements can be made by selecting 1 of each face card (i.e., jack, queen, king) from the pile?

Deriviation :There are 12 face cards. In each possibility there is 3:4 chance of getting a random choice of king, queen, or jack.

Combination or Permutation? combination

Why? Several there are 3 types of face cards and there is only a possibility you willl get a jack, queen, or a king if you select a face card.

2.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?

Deriviation : There are several ways in which you can randomly select each card.

Combination or Permutation? combination

Why: Each time that you shuffle a deck it randomizes the order in which the cards are pulled. Other than that the only way to achieve order is before you shuffle the deck.

3.How many different selections of 3 cards can be made from 12 face cards?

Deriviation: Four cards from ech set would make twelve cards from each deck. 4+4+4=12

Combination or Permutation? combination


Why: There are only face cards left so will have to draw one

 

[Denis]

Re: Probabilty combinations, deriviations, permutations

What's a "pile"? 12 cards?

Your answers are nothing but guesses...
You need to learn "permutations and combinations".

 

[pka]

You can make the selection of the three cards in \(\displaystyle 4^3\) ways.
Do you see that there are 4 ways to select a king?

Once the selection is made, there are \(\displaystyle 3!\) ways to arrange the three cards.

 

[agmoore]

No can you explain the fourth way to get a King.

 

[pka]

No can you explain the fourth way to get a King.

\(\displaystyle \boxed{K\heartsuit}\;;\;\boxed{K\clubsuit}\;;\;\boxed{K\diamondsuit}\;;\;\boxed{K\spadesuit}\)
Count them! There are four.

 

[agmoore]

Sorry this problem has me stressing out I get that now but I need help explaining the combinations and permutations

 

[pka]

Sorry this problem has me stressing out I get that now but I need help explaining the combinations and permutations

Your original post asked this question:

1.How many different arrangements can be made by selecting 1 of each face card (i.e., jack, queen, king) from the pile?

Frankly I don’t think that you understand how ‘cards’ work.
Moreover, I don’t think that you understand the intent of the question.
It says, pick one card from each type: ‘King’, ‘Queen’, ‘Jack’.
There are four of each type: \(\displaystyle 4^3\).
BUT, the question goes on to say “How many different arrangements”.
The answer to that is \(\displaystyle 3!\).
So the complete answer is \(\displaystyle 4^3(3!)\).