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

Question

answer options are

270,725 54,145 121,431 1,082,900 6,497,400

Answer 1

First card has 52 chances to selected, the second one - 51, third - 50, and fourth one - 49 chances.

Their product equals to the number of permutations without repetiiton = 52X51X50X49 = 6,497,400.

But in each set of four cards they can be rearranged in 4!=1x2x3x4 = 24 times. To get the number without replacement yiou have to divide 6,497,400 by 24. It equals 270, 725.

Answer 2

You can use combination: Picking 4 out of 52 gives 52C4 = 270,725