4 cards are drawn in succession and without replacement from a standard deck of 52 cards.  How many sets of 4 cards are possible?

a)54145
b)6497400
c)270725
d)1082900

A

B.

Arrival? 52*51*50*49

the number lessens each time because there is one less card in the deck on each draw.

That was my first guess as well. However, that doesn't take into account duplicate sets.

AH, KH, QH, JH = KH, AH, QH, JH = JH, AH, KH, QH, etc

there are 52 CARDS in a deck. regardless of the face. you only have 52.

the 3 you mention are all the same. they only count as one 4 card set. if you try that pattern B is not enough and its the highest number.

if you want to go that route multiply B by 16(4 cards * 4 places)

103958400

There are 270725 unique [b]sets[/b].  A set has no ordering mathematically speaking, so the answer is "52 choose 4", which is

52!/48!/4! = 52*51*50*49/24 = 6497400/24 = 270725

Why?  There are 52 choices for the first card, 51 for the second, 50 for the 3rd, 49 for the 4th.  That's 6497400 ways.  But there are duplicate sets; you have to count the number of ways to order 4 unique cards.  Again:  4 choices for the first, 3 for the 2nd, 2 for the 3rd, and 1 for the 4th.  That's 24 ways to order 4 unique cards, so you have to divide by 24 in order to not double-count your sets.

If order really is important (so you're not really talking about sets), then the answer is 6497400.

your right, it is 24 not 16. the funny thing is that this question, depending on the rules of the answer can be any of the 4.