Final answer:
To find the number of possible 11-card hands with a 23-card deck, you can use the formula for combinations. The number of 11-card hands is 1,352,078.
Step-by-step explanation:
To find the number of possible 11-card hands with a 23-card deck, we can use the formula for combinations. The formula is given by C(n, r) = n! / (r!(n-r)!), where n is the total number of cards in the deck and r is the number of cards in the hand.
Substituting the values into the formula, we have C(23, 11) = 23! / (11!(23-11)!).
Simplifying further, we get C(23, 11) = 23! / (11!12!).
Calculating the factorial of 23 and the factorials of 11 and 12, we have C(23, 11) = 23 × 22 × 21 × 20 × 19 × 18 × 17 × 16 × 15 × 14 × 13 / (11 × 10 × 9 × 8 × 7 × 6 × 5 × 4 × 3 × 2 × 1 × 12).
After simplifying the expression, we get C(23, 11) = 1352078.