how many 2 card hands are possible with a 26 card deck?
To calculate the number of 2-card hands possible with a 26-card deck, we can use the combination formula.
The number of combinations of n items taken m at a time is given by the formula:
C(n, m) = n! / (m!(n-m)!)
In this case, n is the number of cards in the deck (26) and m is the number of cards in each hand (2).
So, we can substitute the values into the formula:
C(26, 2) = 26! / (2!(26-2)!)
Simplifying this expression further:
C(26, 2) = 26! / (2! x 24!)
To calculate the factorial of a number, we multiply all the numbers from that number down to 1.
26! = 26 x 25 x 24!
Simplifying further:
C(26, 2) = (26 x 25 x 24!) / (2! x 24!)
The 24! terms cancel out:
C(26, 2) = 26 x 25 / 2!
The factorial of 2 (2!) is:
2! = 2 x 1 = 2
So, the final calculation is:
C(26, 2) = 26 x 25 / 2 = 325
Therefore, there are 325 possible 2-card hands with a 26 card deck.
To calculate the number of 2-card hands possible with a 26-card deck, we can use the combination formula.
The combination formula is represented as C(n, k) and calculates the number of ways to choose k items from a set of n items without regard to order.
In this case, we want to find the number of 2-card hands, which means we need to choose 2 cards from a 26-card deck.
Using the combination formula, we have:
C(26, 2) = 26! / (2! * (26-2)!) = (26 * 25) / (2 * 1) = 325
Therefore, there are 325 possible 2-card hands with a 26-card deck.