Harry Marshall
MAE 6127
Group B
01/24/2007
Assignment: Lotto 6/49
Given 49 different numbers: 1 2 3 … 49
players choose 6 numbers on their ticket
Random selection of 6 (order not important) as winner
1st prize: all 6 correct 2nd prize: 5 out of 6 correct
Calculate the probability of winning 1st prize.
How many different tickets? 49C6 = 13,983,816
How many ways to win?
1
probability of 1st prize? 1 out of 13,983,816
2nd prize: 5 out of 6 correct
How many different tickets? 49C6 = 13,983,816
How many ways to win?
6C5 X 43C1 =258
probability of 2nd prize?
258 out of 13,983,816 or 1.845 X 10^5
Manhattan Distance:
Below are the distances done by hand if are streets are bidirectional:
Harry Marshall
MAE 6127
Group B
01/24/2007
Below are the number of paths assuming the streets are bi-directional. In Excel, the
absolute values of both the horizontal and vertical distances from the origin were added.
Notice there are four quadrants of Pascal’s Triangle:
Below are the distances with only 1-way streets:
Harry Marshall
MAE 6127
Group B
01/24/2007
Many of the squares have the same distances as the corresponding intersections on the
two-way street worksheet. Others have values of 2 added to their values. Therefore, cabs
in Manhattan distance must travel a maximum of 2 extra blocks due to the one-way
streets.
One-Way Paths:
Harry Marshall
MAE 6127
Group B
01/24/2007
I did as much as I could by hand without getting dizzy and noticed that the map does not
have its symmetry about the axis as I expected. The top right sdeudo-quadrant seemed to
be the easiest to figure out the paths so there are less paths there. The 3rd or bottom, left
pseudo-quadrant was by far the most difficult since it has the longest mean path distance
and most likely the most complex number of paths.