Answer:
1/5525
Step-by-step explanation:
We now that a standard deck has 52 different cards. Also we know that a standard deck has four different suits, i.e., Spades, Hearts, Diamonds and Clubs. We can find the following cards for each suit: Ace, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, Jack, Queen and King.
Now, the probability of getting any of these cards off the top of a standard deck of well-shuffled cards is 1/52. As we have 4 different sixes, we have that the probability of getting a six is 4/52. When we get a six, in the deck only remains 3 sixes and 51 cards, so, the probability of getting another six later is 3/51. When we get the second six, in the deck only remains 2 sixes and 50 cards, so, the probability of getting the third six is 2/50. As we have independet events, we should have that the probability of getting 3 sixes off the top of a standard deck of well-shuffled cards is
(4/52)(3/51)(2/50)=
24/132600=
12/66300=
6/33150=
3/16575=
1/5525
