SOLUTION: In a certain card game, players are dealt nine cards from a standard 52 card deck. How many hands are possible?

Question 1202739: In a certain card game, players are dealt nine cards from a standard 52 card deck. How many hands are possible?
Answer by math_tutor2020(3817) (Show Source): You can put this solution on YOUR website!

n = 52 cards total
r = 9 selections
I'm not familiar with the rules of this 9-card game, but I'll assume the order doesn't matter.

Since the order doesn't matter, it leads to the nCr combination formula.
n C r = (n!)/(r!(n-r)!)
52 C 9 = (52!)/(9!*(52-9)!)
52 C 9 = (52!)/(9!*43!)
52 C 9 = (52*51*50*49*48*47*46*45*44*43!)/(9!*43!)
52 C 9 = (52*51*50*49*48*47*46*45*44)/(9!)
52 C 9 = (52*51*50*49*48*47*46*45*44)/(9*8*7*6*5*4*3*2*1)
52 C 9 = (13*17*10*7*2*47*46*5*11)/(1)
52 C 9 = 3,679,075,400

Answer: 3,679,075,400 (approximately 3.679 billion)

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