Assignment 15

Problem 3: (combinations 52 6) = 20358520

Problem 9:
a) all hearts: there are 13, so (combinations 13 5) = 1287
b) cards all of the same suit: 
     By symmetry, the number of such hands should be 4 times the
     number of plays in part a), where we did it for hearts. This is
     the same as

         (combinations 4 1) * (combinations 13 5) = 5148,

     since (combinations 4 1) is 4 (choice of one suit from four suits).

Problem 11: 
      (combinations 10 2)
      *
      (combinations 8 2)
      *
      (combinations 12 2)
      *
      (combinations 7 2) = 1746360

Problem 16:
      (combinations 4 1)
      *
      (combinations 13 4)
      *
      (combinations 3 1)
      *
      (combinations 13 2) = 669240

Problem 18: 
a) (combinations 13 7) = 1716
b) (combinations 8 4) * (combinations 5 3) = 700

Problem 30: 
a) (combinations 4 3) * (combinations 48 2) = 4512

b) (combinations 4 3) * (combinations 48 2)
   +
   (combinations 4 4) * (combinations 48 1) = 4560

Problem 34: 
      (combinations 12 4)
      *
      (combinations 8 4)
      *
      (combinations 4 4) = 34650

Problem 36: 
      (permutations 20 2)
      *
      (combinations 18 6) =

      (combinations 20 1)
      *
      (combinations 19 1)
      *
      (combinations 18 6) = 7054320

Problem 37:
      (combinations 42 1)
      *
      (combinations 49 5) = 80089128