You draw two cards from a standard deck of 52 cards without replacing the first one before drawing the second.
To determine the number of possible outcomes when drawing two cards from a standard deck of 52 cards without replacement, you need to consider the concept of combinations.
A combination refers to the selection of items from a larger set where the order of selection does not matter. The formula for calculating combinations is given by:
nCr = n! / r!(n - r)!
Where:
n = total number of items
r = number of items selected
In this case, you want to find the number of combinations when selecting 2 cards from a deck of 52 cards without replacement. Therefore, you need to calculate:
52C2 = 52! / 2!(52 - 2)!
Simplifying the equation:
52C2 = 52! / 2!(50)!
52C2 = (52 * 51) / (2 * 1)
52C2 = 1326
So, there are 1,326 possible combinations when drawing two cards from a standard deck without replacing the first one before drawing the second.