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The task in the image asks to calculate the number of different ways to get specific poker hands using a modified deck. The deck in this problem consists of only the cards ranked 7 through Ace, which means that ranks 2 through 6 have been removed. Let's break down the problem:

### Key points:
- The standard deck has 52 cards, but in this problem, the deck is reduced by removing all cards ranked 2 to 6.
- This leaves the following ranks: 7, 8, 9, 10, Jack, Queen, King, and Ace.
- Each of these ranks has 4 cards (one from each suit: spades, hearts, diamonds, clubs).
- Thus, the modified deck now contains 8 ranks × 4 cards per rank = 32 cards.

The problem asks you to determine the number of ways to get various poker hands using this modified deck. However, it seems like the specific poker hands to calculate are not shown in the image, just the general instruction to calculate combinations for a 5-card hand from this modified deck.

### Step-by-Step Solution for "Any random five cards being dealt":
We will first calculate the number of different ways to deal any random five cards from the modified deck of 32 cards.

To calculate the number of combinations of 5 cards from a deck of 32, we use the **combinations formula**:

\[
C(n, k) = \frac{n!}{k!(n-k)!}
\]

Where:
- \( n = 32 \) (total number of cards in the modified deck)
- \( k = 5 \) (since we are selecting 5 cards)

Let's calculate this now.The number of different ways to deal any random five cards from the modified 32-card deck is **201,376**.

Would you like further clarification, or to continue solving for specific hands like pairs, three-of-a-kinds, etc.?

Here are some questions to expand your understanding:

1. How would the probability change if you were calculating for specific hands like a full house or flush?
2. How does removing cards ranked 2 to 6 affect the overall strategy in this poker scenario?
3. Can you explain why combinations are used here instead of permutations?
4. What would happen if we changed the number of cards dealt (for example, 7-card hands instead of 5)?
5. How would you calculate the probability of getting no pair (all cards of different ranks) in this scenario?

**Tip**: Understanding combinations and probabilities helps in both theoretical and real-world decision-making during games!

Now, we are going to determine the number of ways of getting different hands in Five-Card Poker if we only used certain cards from the deck. You will use a standard 52-card deck, but remove all the cards with ranks 2-6. So, you will only have the cards with ranks 7 through Ace. Determine the number of different ways of getting each of the following hands with this new modified deck: Any random five cards being dealt to you.

Learn how to calculate the number of ways to deal different hands in Five-Card Poker using a modified deck, where cards ranked 2-6 are removed. This detailed explanation covers combinatorics and probability, including the use of the combination formula to find the number of ways to deal five random cards.

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