Question

Inthecardgamebridge,the52cardsaredealtoutequallyto4players—calledEast, West, North, and South. If North and South have a total of 8 spades among them, what is the probability that East has 3 of the remaining 5 spades?

answer is (5c3)(21c10)/(26c13) However; im unclear where 21c10 comes from please explain this especially the 10

Answer 1

Answer)

52 cards are divided equally among 4

52/4 = 13

North and south got 8 spades in total

Now we are left with 5 spades

And 26 cards to be distributed among east and west

We need to find the probability that east has 3 of the remaining 5 spades

Now 13 cards can be distributed among east and west in

26c13 ways

So, total = 26c13

And 3 spades from 5 remaining spades can be distributed to east in 5c3 ways

Now we want only 3 spades with east

So rest of the 10 cards should come from 21 cards which are not spade

21c10

So, favorable outcome would be 5c3*21c10

Required probability is (5c3*21c10)/(26c13)