189k views
4 votes
How many 11​-card hands are possible with a 23​-card ​deck?

User Discolor
by
8.5k points

2 Answers

2 votes

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.

User Martey
by
7.8k points
2 votes
That would be the number of combinations of 11 from 23.

= 23C11 = 23! / (12! * 11!) = 1,352,078 ANswer
User Parmendra Singh
by
8.5k points

No related questions found