If six cards are selected at random (without replacement) from a standard deck of 52 cards, what is the probability there will be no pairs? (two cards of the same denomination)
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The probability that the three cards have no pair is equal to 2112/2550 .
Total number of cards = 52
Probability of first card = 52/52 as any random card can be picked for the first time .
While picking the second card , the card similar to first card cannot be picked .
So , the no. of cards which can be picked = 48 as each card has 3
other cards of same denominaton.
Probability of picking second card = 48/51
The third card cannot be equal to either first or the second card .
So, no. of cards which can be picked = 44
Probability of picking the third card = 44/50
Probability that the three cards picked have no pairs = (52/52) × (48/51) × (44/50)
=> 2112/2550
=> 0.828
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