Assignment 16

Problem 4: 

    Total winning possibilities: 12^4*10^2

    P = 1/(12^4*10^2) = 2073600

Problem 5: P = 1/(10!) = 2.755731922398589E-7

Problem 6: 
     (combinations 4 4)*(combinations 4 2)/(combinations 52 6) = 2.947169047651794E-7

Problem 8: P(1 girl) + P(2 girls) =
     (combinations 5 1)/(2^5) + (combinations 5 2)/(2^5) = 0.46875

Problem 10: P(all male) + P(all female) =
     (combinations 6 3)/(combinations 10 3) +
      (combinations 4 3)/(combinations 10 3) = 0.2

Problem 19: 
a) (combinations 10 3)/(combinations 24 3) = 0.05928853754940711
b) ((combinations 10 3) + (combinations 6 3) + (combinations 8 3))/
	(combinations 24 3) = 0.09683794466403162
c) (10*6*8)/(combinations 24 3) = 0.23715415019762844

Problem 20: 
a) P = 1/(2^10) = 9.765625E-4
b) P = 1 - 1/(2^10) = 0.9990234375
c) P = (combinations 10 6)/(2^10) = 0.205078125

Problem 25: (combinations 11 3)/(combinations 20 3) = 0.14473684210526316

Problem 26: P(2 >= same color) = 1 - P(distinct) =
    1 - (4*5*6)/(combinations 15 3)) = 0.7362637362637363

Problem 29: P = (10^4)/(permutations 40 4) = 0.004559215085530875

Problem 33: P(2 >= same b-day) = 1 - P(distinct) =
     1 - (permutations 365 15)/(365^15) = 0.2529013197636869

Problem 34: P(2 >= same b-day) = 1 - P(distinct) =
     1 - (permutations 365 25)/(365^25) = 0.5686997039694637

Problem 35: P(2 >= same b-month) = 1 - P(distinct) =
     1 - (permutations 12 7)/(12^7) = 0.888599537037037

Problem 36: P(2 >= same b-month) = 1 - P(distinct) =
     1 - (permutations 12 5)/(12^5) = 0.6180555555555556

Problem 37: P(correct) = 1/((combinations 49 5) * 42) = 1.2486089247968838E-8

Problem 38: P(matching four white and powerball) = 
   (combinations 5 4)*(combinations 44 1)*1/
          ((combinations 49 5) * 42) = 2.746939634553144E-6

Problem 39: P(matching two white and powerball) = 
   (combinations 5 2)*(combinations 44 3)*1/
          ((combinations 49 5) * 42) = 0.0016536576600009928

Problem 40: P(matching all white balls and not the powerball) = 
   (combinations 5 5)*(combinations 41 1)/
          ((combinations 49 5) * 42) = 5.119296591667224E-7

Problem 41: P(matching three white balls and not the powerball) = 
   (combinations 5 3)*(combinations 44 2)*(combinations 41 1)/
          ((combinations 49 5) * 42) = 0.004842854575717193