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cool_rashi Goldie

Posted: 6 years ago

Calculate the number (not the probability) of bridge hands which contain the following: (Recall that a Bridge hand consists of 13 cards taken from a standard 52 card deck of playing cards.)
1. a) 5 clubs and 5 hearts
2. b) 4 clubs and 3 cards in each of the other suits
3. c) 7 cards of one suit

Edited by cool_rashi - 6 years ago

akhl IF-Rockerz

Posted: 6 years ago

Originally posted by cool_rashi

Calculate the number (not the probability) of bridge hands which contain the following: (Recall that a Bridge hand consists of 13 cards taken from a standard 52 card deck of playing cards.)
1. a) 5 clubs and 5 hearts
2. b) 4 clubs and 3 cards in each of the other suits
3. c) 7 cards of one suit

Could not reply earlier as I had not visited the forum in many weeks.

1a) There are 13 clubs, 13 hearts

5 clubs can be drawn from 13 clubs in 13C5 ways

5 hearts can be drawn from 13 hearts in 13C5 ways

Remaining 13-5-5=3 cards can be drawn from remaining 52-13-13 = 26 cards in 26C3 ways

No. of bridge hands = 13C5 X 13C5 X 26C3

2b) 4 clubs out of 13 clubs can be drawb in 13C4 ways

Each suit is of 13 cards.

So 3 cards from each of the other suit can be drawn in

13C3 X 13C3 X 13C3 ways

No. of bridge hands = 13C4 x 13C3 X 13C3 X 13C3

3c) There are 4 suits

There are 4 suits,

1 suit can be selected in 4 ways,

7 cards from this suit can be drawn in 13C7 ways

Remaining 13-7=6 cards have to be drawn from remaining 52-13 = 39 cards

This can be done in 39c6 ways

No. of bridge hands = 4 X 13C7 X 39C6

_Pooja_ Newbie

Posted: 6 years ago

Sorry..

Cry

Edited by _Pooja_ - 6 years ago

xLavenderx IF-Sizzlerz

Posted: 5 years ago

P&c ques...muhje dur hi rakho

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