Answer: 0.0000842890
Step-by-step explanation:
Given that :
Number of cards in a deck = 52
Number of hearts in a deck = 13
Probability of being dealt 6 hearts :
Probability = (required outcome / Total possible outcomes)
Required outcome = choosing 6 hearts from a possible 13
13C6:
Recall : nCr = (n! / (n-r)!r!)
13C6 = 13! / (13-6)!6!
13C6 = 13! / 7!6!
13C6 = (13*12*11*10*9*8)/(6*5*4*3*2*1)
13C6 = 1235520 / 730
13C6 = 1716
Total possible outcomes :
52C6 = 52! / (52-6)!6!
52C6 = 52! / 46!6!
52C6 = (52*51*50*49*48*47)/(6*5*4*3*2*1)
52C6 = 14658134400 / 720
52C6 = 20358520
Hence,
P(6 hearts) = 1716 / 20358520
P(6 hearts) = 0.0000842890
