203k views
14 votes
How many combinations of 3 playing cards (from a 52-card deck) exist?

25,000
1,649
523

its not 22,100 btw....

User SashikaXP
by
8.1k points

2 Answers

8 votes

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.

User Thomh
by
9.0k points
5 votes
523 should be your answer
User Alex Char
by
7.9k points

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