Question

1. From a standard deck of 52 cards, how many 5-card poker hands are there, that have at least 3 spades? (Hint: divide the problem in cases: a poker hand has 3 spades, 4 spades, 5 spades.)

Answer 1

Angwer We have a standard deck of 52 Cards. 5 Card poker hands having atleast 3 Spades a Casel having exactly 3 Spades and 2 other No. of poker hands l select 3 Cards from 13 spade cards and) I select 2 cards from 39 other Cards / No. of ways or Combinations of or different i I things from ndifferent things = ng = n! na-! 13! 39! 13x12x 11 x 39x38 = 211926 2110 21 37! 6 2 Case 2 having exactly 4 spate Card and I other No of combination of u Spare Part 3 134 No. of ways to select one other Card 396, Total = Byx 396 13! 391 419! 1381 Scanned with CamScanner

13x12x11x10 x4 24 x a x 39 27885 Case 3. having all 5 spade Cards = 13cd No. of Combination of s spades out of 13 spades 13! 13! 13x12x11x 16x9 = 518! 5! = 13x12x ll x 10 x 9 q = 1287 120 Total 5 Card boker hands 211926+27885 +1287 Possible = |241098 Anguer Scanned with CamScanner