I don't even know what this means. Please help
Five cards are drawn in succession, without replacement, from a standard deck of 52 cards. How many sets of five cards are possible?
A. 500
B. 12,994,800
C. 2,598,960
D. 433,160
combinations of five cards out of 52 cards:
C(52,5)= 52!/[5!(52-5)!]
= 52!/[5!(47!)]
= 52*51*50*49*48/(5*4*3*2)
= 52*51 *10*49*2
= 2,598,960 remarkable
To find the number of possible sets of five cards that can be drawn from a standard deck of 52 cards without replacement, we can use the concept of combinations.
The number of combinations of n objects taken r at a time, denoted as C(n, r) or nCr, can be calculated using the formula:
C(n, r) = n! / (r! * (n - r)!)
In this case, we want to find the number of combinations of 52 cards taken 5 at a time. Therefore, the formula becomes:
C(52, 5) = 52! / (5! * (52 - 5)!)
Simplifying this expression, we can calculate the factorial terms:
52! = 52 * 51 * 50 * 49 * 48 * ... * 1
5! = 5 * 4 * 3 * 2 * 1
(52 - 5)! = 47 * 46 * 45 * ... * 1
After evaluating these factorials, we can substitute the values back into the formula:
C(52, 5) = (52 * 51 * 50 * 49 * 48) / (5 * 4 * 3 * 2 * 1 * 47 * 46 * 45 * ... * 1)
Finally, we simplify this expression to find the total number of possible sets of five cards:
C(52, 5) = 2,598,960
Therefore, the answer is C. 2,598,960.