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

card-gamescombinationspermutationsprobability

A simple question but the solution is confusing me. The answer I obtained was
$$p = 3! \times 4/52 \times 4/51 \times 4/50$$

The first 3! is for the order of king, queen, jack. $4/52$ is the probability of drawing a king, $4/51$ is the probability of drawing a queen after a king is drawn and $4/50$ is the probability of drawing a jack once both king and queen are drawn. But the book takes the solution as

$$p = 3! \times 4/52 \times 3/51 \times 2/50$$

Can anyone please explain how this comes?

Thanks in advance.

Best Answer

The probability of drawing a king, queen, and jack is;

$$\frac{3! 4^3}{52\,51\,50}$$

The probability of drawing a king, queen, and jack of different suits is:

$$\frac{3!~4!}{52\,51\,50}$$