# STATISTICS

#### JAY-D

##### New member
this my 1st statistics class. i am in the army and away from my post. I am just in college taking classes on line. I need to take this class, but it is killing me. this is the 1st statistics class i have taken. i know for many this may be eash for me it's hard. please give me some help. Here is the question. I've looked at the formulas over and ove and can't figure them out. please show me how you got the answer.

What is the probability of getting 3 kings when 4 cards are drawn from an ordinary deck?

#### galactus

##### Super Moderator
Staff member
I assume you are familiar with cards enough to know there are 52 in the deck and 4 Kings.

Without replacement, the probability of the first King is 4/52. The second would be 3/51, the third would be 2/50, and the last card can be any other card of the 48 cards out of the remaining 49(one is the last King). But, these can be drawn in varying orders, such as KKCK, KCKK, etc, there are 4 different arrangements.

So, the probability is $$\displaystyle 4(\frac{4}{52})(\frac{3}{51})(\frac{2}{50})(\frac{48}{49})$$

We can also use combinations by noting we are choosing 3 of the 4 Kings and 1 of the other 48 cards.

The denominator is the total number of ways to choose 4 from 52 cards.

$$\displaystyle \frac{\binom{4}{3}\binom{48}{1}}{\binom{52}{4}}$$

Are you familiar with that notation?. It refers to combinations.

Both methods will result in the same probability