Two cards are drawn from a well-shuffled ordinary deck of 52 cards. In how many ways can one draw two cards without replacement?
Clearly, that is 52C2
Doesn't matter whether the deck is shuffled or not. Same 52 cards!
To solve this problem, we can use the concept of permutations.
When you draw the first card, there are 52 possibilities since you can choose any of the 52 cards in the deck. After you draw the first card, there are 51 cards left in the deck.
When you draw the second card, there are now 51 possibilities because one card has already been drawn.
To find the total number of ways to draw two cards without replacement, we multiply the number of possibilities for the first card (52) by the number of possibilities for the second card (51).
Therefore, the total number of ways to draw two cards without replacement is 52 * 51 = 2,652.