Question

An experiment consists of dealing 6 cards from a standard 52-card deck. What is the probability of being dealt 6 hearts?

Answer 1

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