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# I have a deck of cards. What is the chance

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I have a deck of cards. What is the chance if I draw 4 cards, all of them are a distinct type? (Ace,2,3,5,6,7,8,9...King)

Nov 16, 2020

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I have a deck of cards. What is the chance if I draw 4 cards, all of them are a distinct type? (Ace,2,3,5,6,7,8,9...King)

The first card can be anything                        1

There's a 3 in 51 chance of drawing                        3

one of the three remaining cards                    1  •  ——

51

There's a 2 in 50 chance of drawing                         3          2

one of the two remaining cards                        1  •  ——  •  ——

51        50

There's a 1 in 49 chance of drawing                           3          2          1

the last remaining card                                      1  •  ——  •  ——  •  ——

51        50        49

Multiply all the individual chances and

the answer is the chance of all of them                  6                                              3

happening simultaneously                                ————    which reduces to    ————

122,500                                     61,250

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Nov 17, 2020