In how many ways can four spades be drawn from a standard deck of playing cards with out replacement?
52*51*50*49=6,497,400
To find the number of ways four spades can be drawn from a standard deck of playing cards without replacement, we can break down the problem into steps:
Step 1: Determine the total number of spades in the deck.
In a standard deck of playing cards, there are 13 spades (Ace to King).
Step 2: Calculate the number of ways to choose four spades from the available options.
We can use combinatorics to calculate this. The formula for choosing "k" items from a set of "n" items is given by the combination formula:
C(n, k) = n! / (k!(n-k)!)
In this case, we need to calculate C(13, 4). Plugging the values into the formula, we have:
C(13, 4) = 13! / (4!(13-4)!)
= 13! / (4! * 9!)
= (13 * 12 * 11 * 10) / (4 * 3 * 2 * 1)
= 715
Therefore, there are 715 ways to draw four spades from a standard deck of playing cards without replacement.