an ordered sequence of three cards is dealt from a standard deck of 52 cards. How many sequences consist of all red or all face​ cards?

A standard deck of 52 cards consists of 26 red cards (13 hearts and 13 diamonds) and 12 face cards (4 jacks, 4 queens, and 4 kings).

To determine how many ordered sequences of three cards consist of either all red cards or all face cards, we break the problem into two cases and then combine them:

### Case 1: All Red Cards
There are 26 red cards. To form a sequence of 3 cards, where all cards are red, we need to choose 3 cards from these 26 red cards. Since the sequence is ordered, the number of ways to do this is simply:

\[
26 \times 25 \times 24 = 15,600
\]

### Case 2: All Face Cards
There are 12 face cards (4 jacks, 4 queens, and 4 kings). To form a sequence of 3 cards, where all cards are face cards, we need to choose 3 cards from these 12 face cards. The number of ways to do this is:

\[
12 \times 11 \times 10 = 1,320
\]

### Total Number of Sequences
Since the two cases (all red cards and all face cards) are mutually exclusive, we add the results of both cases together to get the total number of sequences:

\[
15,600 + 1,320 = 16,920
\]

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

Would you like any further details or have any questions?

Here are 5 related questions:
1. How many sequences consist of exactly two red cards and one face card?
2. How many sequences consist of exactly one red card and two face cards?
3. What is the probability of drawing an all-red sequence from a deck of 52 cards?
4. How many ordered sequences of three cards are there in total from a standard deck?
5. How many sequences consist of all black cards?

**Tip:** Always break complex counting problems into smaller, manageable cases to simplify your calculations.

An ordered sequence of three cards is dealt from a standard deck of 52 cards. How many sequences consist of all red or all face​ cards?

Learn how to calculate the number of ordered sequences of three cards consisting of either all red or all face cards from a standard deck of 52 cards. This problem involves combinatorics and permutations, suitable for students in Grades 10-12.

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