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The answer is 8,648,640 in 674,274,182,400 or approximately 0.128%.

To pull seven spades in a row from a deck of 52 cards may be translated as follows:

In a deck of 52 cards there are 13 spades, so 13 chances to pull a spade or 13/52.

After pulling one spade, there are 12 spades left and 51 cards left, so 12 chances to pull a spade or 12 / 51.

After pulling the second spade, there are 11 spades left and 50 cards left, so 11 chances to pull a spade or 11 / 50.

Continuing the above logic to the natural conclusion, we get the following multipliers:

13 / 52 * 12 / 51 * 11 / 50 * 10 / 49 * 9 / 48 * 8 / 47 * 7 / 46

which is equal to 8,648,640 / 674,274,182,400 or approximately 0.128%.

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Q: What is the probability of pulling 7 spades in a row from a deck of 52 cards?
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