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Two cards are randomly drawn from a well shuffled pack of 52 cards one after the other without replacement. What is the probability that both of them are non-face cards of different suit and different face value. (Note ∶ Only King, Queen and Jack are face cards. The face value of the card is the number displayed on the card. Ace has the face value to 1)?

Two cards are randomly drawn from a well shuffled pack of 52 cards one after the other without replacement. What is the probability that both of them are non-face cards of different suit and different face value. (Note ∶ Only King, Queen and Jack are face cards. The face value of the card is the number displayed on the card. Ace has the face value to 1)? Correct Answer 90/221

The number of ways in which two cards can be drawn from a pack of 52 cards one after another without replacement = 52 × 51

Out of 52 cards, 12 cards are face cards and the remaining 40 are non - face cards

These 40 cards are of 4 different suits or each suit has 10 non-face cards

The first card can be selected in 40 different ways

The second card cannot have same face value and same suit

There are 9 other cards having same suit as the first card and 3 other cards having same face value as the first card (total 12)

The second card cannot be same as the first card or any of these 12

The second card can be drawn in 40 - 13 = 27 different ways

Required Probability = (40 × 27)/(52 × 51) = 90/221

∴ Required Probability = 90/221

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