Two jokers have been added to a standard deck of cards.  In how many ways can you deal out five face cards from this new deck?

To determine the number of ways to deal five face cards from a standard deck with two added jokers, we first break down the components of the deck and the problem.

### Step 1: Breakdown of the deck
- A standard deck has 52 cards, including **12 face cards** (4 Jacks, 4 Queens, 4 Kings).
- Two additional **jokers** are added to the deck, bringing the total number of face cards to **14 face cards**.

So, there are 12 face cards plus 2 jokers, for a total of **14 possible face cards** to choose from.

### Step 2: Dealing 5 face cards
We need to select 5 cards from these 14 face cards. The number of ways to choose 5 cards from a set of 14 is given by the combination formula:

\[
\binom{14}{5} = \frac{14!}{5!(14-5)!} = \frac{14!}{5!9!}
\]

### Step 3: Calculating \(\binom{14}{5}\)

First, calculate \(14!/(9! \cdot 5!)\):

\[
\binom{14}{5} = \frac{14 \times 13 \times 12 \times 11 \times 10}{5 \times 4 \times 3 \times 2 \times 1} = \frac{240240}{120} = 2002
\]

Thus, there are **2002 ways** to deal 5 face cards from this new deck.

### Final Answer:
There are **2002 ways** to deal 5 face cards from a deck with 12 face cards and 2 jokers.

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**Related Questions:**
1. How many ways can you deal 5 cards from the full 54-card deck (including jokers)?
2. What if no jokers are allowed in the hand? How many ways can 5 face cards be dealt then?
3. What if at least one joker must be in the hand? How many ways can this be done?
4. How does the solution change if one more joker is added to the deck (making it 3 jokers)?
5. How many different 5-card hands can be dealt from the entire deck if all cards (not just face cards) are allowed?

**Tip:** Always start by understanding the structure of the deck and the types of cards before diving into calculations.

Two jokers have been added to a standard deck of cards. In how many ways can you deal out five face cards from this new deck?

Solve a combinatorics problem where two jokers are added to a standard deck of cards. Learn how to calculate the number of ways to deal five face cards using the combination formula. Suitable for students in Grades 9-12.

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