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)
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
.
