Playing Cards probability problem

Question

From a pack of 52 playing cards, three cards are drawn at random.Find the probability of drawing a king , a queen and jack.?

Answer 1

probability of getting a king on your first draw is 4/52.

probability of getting a queen after a king on your second draw 4/51

jack after a king and a queen 4/50

So the probability of getting a king, then a jack, and then a queen is (4*4*4)/(50*51*52).

There are six orders that give you a king, a queen and a jack.

KQJ, KJQ, QKJ, QJK, JKQ, JQK

So, we take the original probability and multiply it by 6.

6*(4*4*4)/(50*51*52) = 16/5525 $\approx$ .29%

Answer 2

Another way to solve would be

The number of ways you can select a king, queen or a jack for each of the three cards= $${4\choose1}$$

The total number of ways you can select three cards from the deck = $${52\choose3}$$

Required Probability = $$\frac{{4\choose1}{4\choose1}{4\choose1}}{{52\choose3}} = \frac{64}{22100} = \frac{16}{5525}$$