How many 18-card hands, dealt from a standard 52 card pack, contain exactly 9 spades and exactly 3 aces?

Monday, 22 April 2019

8:53 PM

How many 19-card hands, dealt from a standard 52 card pack, contain exactly 11 spades and exactly 2 aces? comb (12, 11) *comb (3, 2) k comb (36, 6) +comb (12, 10) *comb (3, 1) *comb (36, 7) 12c3C236C6

 

 

 

Consider two cases: Total number of hands, with 12 Spades and 3 Aces but notthe Ace of Spades is: 12 is the number ofways to choose 12 Spades, 12 3 is the number of ways to choose 3 Aces, 3 36 is the number of ways to choose the remaining cards. 2 Total number of hands, with 12 Spades and 3 Aces includingthe Ace of Spades is: 12 is the number of ways to choose the other 11 Spades, 11 3 is the number of ways to choose the other 2 Aces, 2 36 is the number of ways to choose the remaining cards. 3 Add the totals for these cases to produce the total number of hands. t) (326) , where , where

 

Created with Microsoft OneNote 2016.