This exercise refers to a standard deck of playing cards. Assume that 5 cards are randomly chosen from the deck.

How many hands contain 4 jacks?

A standard deck of playing cards consists of 52 cards, including 4 Jacks. To calculate how many 5-card hands contain 4 Jacks, we need to determine how many ways to choose 4 Jacks from the 4 available and 1 non-Jack card from the remaining 48 cards in the deck.

### Step-by-step breakdown:

1. **Choosing 4 Jacks**:  
   There is only 1 way to choose all 4 Jacks from the 4 Jacks in the deck (since they all must be selected). This can be expressed mathematically as:
   \[
   \binom{4}{4} = 1
   \]
   
2. **Choosing 1 other card**:  
   Since we've already chosen the 4 Jacks, there are 48 other cards left in the deck (52 total cards minus 4 Jacks). We need to choose 1 card from these remaining 48 cards. The number of ways to do this is:
   \[
   \binom{48}{1} = 48
   \]

### Final Calculation:
Thus, the total number of hands that contain exactly 4 Jacks is:
\[
1 \times 48 = 48
\]

So, there are **48 hands** that contain exactly 4 Jacks.

Would you like further details on this or related questions?

Here are some related questions to explore:

1. How many ways can you get 3 Jacks in a 5-card hand?
2. What is the probability of getting exactly 4 Jacks in a 5-card hand?
3. How many 5-card hands can be formed from a deck of 52 cards?
4. How many hands contain no Jacks at all?
5. How many hands contain exactly 1 Jack?

**Tip:** Always break problems like these down into separate steps to simplify counting and ensure accuracy.

This exercise refers to a standard deck of playing cards. Assume that 5 cards are randomly chosen from the deck. How many hands contain 4 jacks?

Learn how to calculate the number of 5-card hands that contain exactly 4 Jacks in a standard 52-card deck. This problem explores combinatorics, using the binomial coefficient formula to count possible combinations. Perfect for students in Grades 9-12.

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