Answer:
Explanation:
To determine the number of combinations of 3 playing cards from a standard 52-card deck, we can use the formula for combinations, which is given by:
C(n, k) = n! / (k!(n-k)!)
Where n is the total number of items (in this case, the number of cards in the deck) and k is the number of items chosen (in this case, 3 cards).
Plugging in the values:
n = 52 (total number of cards in the deck)
k = 3 (number of cards chosen)
C(52, 3) = 52! / (3!(52-3)!)
Calculating the factorial terms:
52! = 52 x 51 x 50 x ... x 3 x 2 x 1
3! = 3 x 2 x 1
(52-3)! = 49! = 49 x 48 x ... x 3 x 2 x 1
Simplifying the equation:
C(52, 3) = 52 x 51 x 50 / (3 x 2 x 1)
Cancelling out the common factors:
C(52, 3) = (52 x 17 x 25) / (3 x 2 x 1)
C(52, 3) = 22,100
Therefore, there are 22,100 combinations of 3 playing cards that can be chosen from a 52-card deck.