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The probability of dealing the Ace of Spades from a normal 52 card deck is 1 in 52. The probability of dealing the King of Spades next is 1 in 51. The probability of dealing the Queen of Spades next is 1 in 50.

The probability of drawing those three cards in that order is the product of those probabilities, which is 1 in 132,600. This is the same as the number of permutations of N (52) things taken P (3) at a time, which is stated as N! - P! (52 * 51 * 50)

If you did not care what order the cards were dealt in, but still wanted to know the probability of getting the Ace, King, and Queen of Spades, then you would be talking about the combinations of N (52) things taken P (3) at a time, which is stated as (N! - P!) / (N - P)! (52 * 51 * 50 / 3 / 2 / 1). The probability in this case is 1 in 22,100.

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Q: Probability of dealing ace king and queen of spades in that order when dealing only 3 cards?
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What is the probability of dealing an ace king and queen in that order when dealing only three cards?

Assuming you mean from a standard 52-card deck of four suits, there is a 4/52 chance of first dealing an ace, a 4/51 chance of secondly dealing a king and a 4/50 chance of dealing a queen. Together, these mean there is a 64/132600, or 8/16575 or 0.04826546% chance of dealing the desired cards in order.


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