a standard deck of 52 cards without replacement, how many different outcomes are possible?

To find the number of different outcomes when drawing cards from a standard deck of 52 cards without replacement, we use the concept of permutations.

Each time a card is drawn, the number of cards in the deck decreases by 1. Therefore, for the first card drawn, there are 52 possibilities. For the second card drawn, there are 51 possibilities remaining, and so on.

The total number of different outcomes can be calculated by finding the product of the number of possibilities for each draw:

52 \times 51 \times 50 \times \ldots \times 3 \times 2 \times 1

This is known as the factorial of 52, denoted as 52! .

Therefore, the total number of different outcomes when drawing cards from a standard deck of 52 cards without replacement is:

\boxed{52! = 8.0658175 \times 10^{67}}