To solve this problem, we need to determine how many ordered sequences of three cards can be dealt from a deck where all cards are either red or face cards.

A standard deck of 52 cards consists of:

• 26 red cards (13 hearts and 13 diamonds)
• 12 face cards (3 face cards in each of the 4 suits: hearts, diamonds, clubs, and spades)

We will break the problem into two cases:

Case 1: All Red Cards

There are 26 red cards in the deck. We need to select 3 cards from these 26 red cards, and since the sequence is ordered, the number of possible sequences is given by the permutation of 3 cards from 26:

$P(26, 3) = 26 \times 25 \times 24 = 15,600$

Case 2: All Face Cards

There are 12 face cards in total. Similarly, we need to select 3 face cards from these 12, and since the sequence is ordered, the number of possible sequences is:

$P(12, 3) = 12 \times 11 \times 10 = 1,320$

Total Number of Sequences

To find the total number of sequences that consist of all red or all face cards, we sum the results from the two cases:

$\text{Total Sequences} = 15,600 + 1,320 = 16,920$

So, the total number of ordered sequences consisting of all red cards or all face cards is 16,920.

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Would you like more details or have any questions about this solution?

Here are some related questions:

1. How many sequences of three cards can be dealt if all the cards are red?
2. How do permutations differ from combinations in probability problems?
3. What is the probability of getting an all red sequence in a 3-card draw?
4. How can we calculate the number of ways to choose 3 cards from a deck that satisfies certain conditions?
5. How does the ordered nature of the sequence affect the calculation?

Tip: In problems involving ordered selections from a set, remember that permutations account for order, while combinations do not.