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To find probabilities in games like blackjack, it's essential to understand the concept of combinations. The combination formula helps us determine the number of ways to choose a subset of items from a larger set. For a blackjack hand, we'll use the combination formula \( \binom{n}{k} \), where \( n \) is the total number of items, and \( k \) is the number of items to choose. 
For example, to find the number of ways to choose 2 cards from a 52-card deck, we use \( \binom{52}{2} = \frac{52 \times 51}{2 \times 1} = 1326 \). This tells us there are 1326 possible 2-card combinations in a standard deck.
It's crucial to note that the combination formula is different from permutations. Combinations do not consider the order of selection, while permutations do.

In blackjack, the goal is to achieve a hand value as close to 21 as possible, without exceeding that value. A blackjack hand is specifically an Ace paired with a 10-point card (10, Jack, Queen, King).
To determine the probability of being dealt a blackjack hand, we start by identifying all winning combinations. We have 4 aces and 16 ten-point cards. There are \( 4 \times 16 = 64 \) possible blackjack hands.
Next, we've already calculated that there are 1326 possible 2-card combinations in the whole deck. Hence, the probability of getting a blackjack hand is \( \frac{64}{1326} \). After simplifying, this fraction becomes \( \frac{32}{663} \).
Blackjack probabilities can also be expressed as percentages for easier understanding. By converting this fraction to a percentage, we get approximately 4.8%.

Simplifying fractions is essential in probability to make the results clearer and more concise. The original fraction we obtained was \( \frac{64}{1326} \), which can be a bit unwieldy. By finding the greatest common divisor (GCD) of the numerator and the denominator, we can simplify the fraction.
For \( \frac{64}{1326} \), the GCD is 2. So, we divide both the numerator and the denominator by 2, resulting in \( \frac{32}{663} \). This simplified fraction is much easier to work with and interpret.
Fraction simplification not only helps in easier calculation but also aids in better comparison and understanding of probabilities.

After finding the simplified fraction for the probability, it's often useful to convert that fraction into a percentage. Percentages are more intuitive and easier for most people to understand.
To convert a fraction to a percentage, you multiply it by 100. For the simplified fraction \( \frac{32}{663} \), we multiply by 100: \( \frac{32}{663} \times 100 \approx 4.8\% \).
This tells us that approximately 4.8% of all possible 2-card hands dealt in blackjack will be winning blackjack hands. Understanding percentage calculation is crucial for interpreting statistical probabilities in a clear and concise manner.