Note that we can draw the first King(K), then Queen(Q) and then Jack(J). That means the sequence of drawings is (K,Q,J)(K,Q,J). Therefore we have 6 such a sequence of drawing cards:

(K,Q,J), (K,J,Q), (Q,K,J), (J,K,Q), (Q,J,K), (J,Q,K)

Note that each such events are equally likely. Thus in order to find the required answer we first consider one such case, say K,Q,J. Then the required probablity will be: P = 6 * P(K, Q, J)

Let us first find the probability of drawing card first a King(K), then a Queen(Q) and then a Jack(J).

The probability of drawing a King in the 1st draw is Total Number of King / Total Number of Aviliable Cards = 4 / 52

Since we can not replace the card, thus for the second draw we have total 51 cards available.

The probability of drawing a Queen in the 2nd draw is: Total Number of Queen / Total Number of Aviliable Cards = 4 / 51

Since we can not replace the card, thus for the second draw we have total 50 cards available.

The probability of drawing a Jack in the 3rd draw is: Total Number of Jack / Total Number of Aviliable Cards = 4 / 50

Thus the probability of drawing card first a King(K), then a Queen(Q) and then a Jack(J) is given by:

P(K, Q, J) = (4 / 52) * (4 / 51) * (4 / 50)

Hence the required probablity is: \(6 * P(K, Q, J) = \frac{6 * 4^{3}}{52 * 51 * 50}\)

(K,Q,J), (K,J,Q), (Q,K,J), (J,K,Q), (Q,J,K), (J,Q,K)

Note that each such events are equally likely. Thus in order to find the required answer we first consider one such case, say K,Q,J. Then the required probablity will be: P = 6 * P(K, Q, J)

Let us first find the probability of drawing card first a King(K), then a Queen(Q) and then a Jack(J).

The probability of drawing a King in the 1st draw is Total Number of King / Total Number of Aviliable Cards = 4 / 52

Since we can not replace the card, thus for the second draw we have total 51 cards available.

The probability of drawing a Queen in the 2nd draw is: Total Number of Queen / Total Number of Aviliable Cards = 4 / 51

Since we can not replace the card, thus for the second draw we have total 50 cards available.

The probability of drawing a Jack in the 3rd draw is: Total Number of Jack / Total Number of Aviliable Cards = 4 / 50

Thus the probability of drawing card first a King(K), then a Queen(Q) and then a Jack(J) is given by:

P(K, Q, J) = (4 / 52) * (4 / 51) * (4 / 50)

Hence the required probablity is: \(6 * P(K, Q, J) = \frac{6 * 4^{3}}{52 * 51 * 50}\)