If you are dealt 

4 cards from a shuffled deck of 52​ cards, find the probability that all 4 cards are picture cards

To calculate the probability of being dealt 4 picture cards from a shuffled deck of 52 cards, we proceed as follows:

### Step 1: Count the number of picture cards in a deck
A standard deck of 52 cards has 3 picture cards (Jack, Queen, King) in each of the 4 suits. Therefore, there are:

\[
3 \times 4 = 12 \text{ picture cards}
\]

### Step 2: Total combinations for 4 cards from 52 cards
The total number of ways to choose 4 cards from 52 cards is given by the combination formula:

\[
\binom{52}{4} = \frac{52!}{4!(52-4)!} = \frac{52 \times 51 \times 50 \times 49}{4 \times 3 \times 2 \times 1} = 270725
\]

### Step 3: Favorable combinations for 4 picture cards from 12 picture cards
The number of ways to choose 4 picture cards from the 12 picture cards is:

\[
\binom{12}{4} = \frac{12!}{4!(12-4)!} = \frac{12 \times 11 \times 10 \times 9}{4 \times 3 \times 2 \times 1} = 495
\]

### Step 4: Calculate the probability
The probability is the ratio of favorable outcomes to total outcomes:

\[
P(\text{4 picture cards}) = \frac{\binom{12}{4}}{\binom{52}{4}} = \frac{495}{270725}
\]

Simplify:

\[
P(\text{4 picture cards}) \approx 0.00183
\]

### Final Answer:
The probability of being dealt 4 picture cards is approximately **0.183%**.

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Do you want more details or examples? Here are 5 related questions:

1. What is the probability of being dealt 2 picture cards and 2 non-picture cards?
2. How many ways can you select 3 cards of the same suit from a deck?
3. What is the probability of being dealt exactly 1 Ace in a hand of 5 cards?
4. How does the probability change if jokers are included in the deck?
5. What are the odds of being dealt all cards from the same suit in a hand of 4 cards?

**Tip:** When solving problems involving probabilities and combinations, break the problem into clear steps to avoid confusion.

If you are dealt 4 cards from a shuffled deck of 52 cards, find the probability that all 4 cards are picture cards.

Explore how to calculate the probability of being dealt 4 picture cards from a standard deck of 52 cards. This problem involves combinatorics and probability concepts, using the combination formula and fundamental probability principles. Perfect for high school students in Grades 9-12.

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