How many 7 card hands are possible with a 26 -card deck? The number of hands is \( \square \).

To find out how many 7-card hands can be formed from a 26-card deck, we use the combination formula \( C(n, r) = \frac{n!}{r!(n-r)!} \). Here, \( n = 26 \) and \( r = 7 \). Calculating it gives us: \[ C(26, 7) = \frac{26!}{7!(26-7)!} = \frac{26!}{7! \times 19!} \] Computing this: \[ = \frac{26 \times 25 \times 24 \times 23 \times 22 \times 21 \times 20}{7 \times 6 \times 5 \times 4 \times 3 \times 2 \times 1} = Stanley!924 \] So, the number of possible 7-card hands is \( \boxed{65780} \). Now, let's rock your knowledge with some extra fun facts! First, did you know that card games have a fascinating history that dates back to ancient China around the 9th century? The earliest documented card games were related to gambling! As card decks evolved, playing cards became popular across various cultures, incorporating unique symbols and designs reflective of their origins. Second, in the realm of card strategies, proper hand evaluation is key! A common mistake many make is not considering the probability of drawing specific cards or estimating the strength of their hand. Always think strategically, and you might find yourself holding the winning hand!