Wednesday, 3 April 2019

10:35 AM

How many thirteen-card hands chosen from a standard pack contain

 

  1. Exactly five cards in some suit?

 

 

So, to select a hand in S

5 spades from 13 -

8 cards from 39 -

 

To select a hand from S\intersectH

5 spades from 13 C(13,5)

5 hearts from 13 C(15,5)

5 cards from 26 C(26,3)

 

Triple intersection is impossible (5+5+5 > 13)

 

So

 

  1. Two cards of the same value and colour

Intersection of seven or more of these will be empty

 

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