From standard pack of 52 cards, 3 cards are drawn at random without replacement. The probability of drawing a king, a queen and a jack in order is

The correct answer is \(\frac{8}{16575}\)

Key Points

• The probability of drawing a king, a queen and a jack in order is the product of the probabilities of drawing each card. 
• There are 4 kings, 4 queens, and 4 jacks in a standard deck of 52 cards, so the probability of drawing any one of them is 4/52.
  • The first card can be any of the 3 cards in order. The probability of drawing a king first is \(\frac{4}{52}\). 
  • The second card can be either a queen or a jack, but it cannot be the same as the first card. 
• There are 4 queens or jacks left, and 51 cards in total, so the probability of drawing the second card is \(\frac{4}{51}\). 
• The same logic applies for the third card, and the probability of drawing a queen or a jack is \(\frac{4}{50}\).
  • Therefore, the probability of drawing a king, a queen, and a jack in order is \(\frac{4}{52} * \frac{4}{51} *\frac{4}{50} = \frac{8}{16575}\)}

Additional Information

• The number of each card in the deck affects the probability of drawing them.
• The order of drawing the cards affects the final probability.
• This problem assumes that the cards are drawn without replacement, which means that once a card is drawn, it is not returned to the deck.
• The problem calculates the probability of drawing the cards in a specific order, but there are other ways to calculate the probability of drawing a specific combination of cards, regardless of order.