Question

At the bridge table, there are 4 players, called North, East, South, and West. From the 52 card deck, each player gets a set of 13. The cards have a suit from♠,♦,♣,♥, and a rank from A,2,3,4,5,6,7,8,9,10,J,Q,K. Two bridge tables are different, if some card is at a different player.

a) What is the number of bridge tables?

b) What is the number of bridge tables, in which every player has a card of every ranking his hand?

c) What is the number of bridge tables, in which every player has cards from only one suit?

d) What is the number of bridge tables, in which every player has an Ace?

Answer 1

Şolutºon : Given that * At the bridge table, thexare 4 players, Called in North, East South, and West → From the 12 caod deck; each plager gets a set of 15. the cards have a suit from 2 , 4 and a Šank from A,2,3,4,5,6,7,8,9,10, j, Q, k. 7. Two bridge tables are different, if some card as at a diffešent player. (a): Now; → we have 13 cards to north then 13 cards to east. 13 cards to sound and 13 cards to west. : each time we have a different table; . Total different x/ways of giving e of Total ways. (total different wnuel (Total different ways Is y/of giving 13 cards to to North 39) giving is cards I least out of I i3 cards to the maining south out of rem 26)

l. Total ways - 52 39 26 cxc xoc 13 13 13 (b): Here, → Doing same thing as shown in part (a) and giving all A's between North, South, west, east then giving a's, .3's, ...k's, - Total ways (ways of giving / ways of giving ways of giving an A . lat. A to North J an A to cast to South of dem 2 of rem z cards ( cards) I ways of giving ways of giving ? / ways of giving ) Mas k to North Ya k to east x a k to South of I lof rem o cards/ (remaining 2 Caod 3) - (4x3*2) x (HX3X2)X ---- - * [4x3X2) :(482x2)13

= (4x16) 3 2 (24315 Total wegs : (184) (C): ay we have 4 choices giving north out of those 4 Suits, similarly for east, we would have z Suits, for South we will have 2 and 4 the suit to west. Therefore total ways = 4X 3 X QX! = 12x2x) : 1282 -24 Total ways - 24

giving each player to Ace, then give id words out of remaining 48 to North, 12 out of remaining 36 to east; ld out of remaining, 24 to South and then remaining ones to west, Hence ale uge 3 (trys) 149 149 cm) X 3XQXLX Giving A's. 148 - (24) , c x u iz 36 C X 12. 0 24 c. 12) : Total ways an / 48. 36 24 c. x . c X T 12 12 12