«GreetingLine»
Spring 2007
MAE 6127
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? 49 C6  13, 983, 816
How many ways to win?
1
Probability of 1st prize?
1/13,983,816
2nd prize: 5 out of 6 correct
How many different tickets?
How many ways to win?
Probability of 2nd prize?
C6  13, 983, 816
6 C5 x 43 C1  6x43  258
258
43

13983816 2330636
49
The assignment is to calculate the probability of winning the Florida lotto, which
consists of selecting six out of 49 numbers ( 1 to 49 ), as well as winning the second prize
which consists of selecting five out of six correct numbers.
The first step is to calculate how many different tickets would be available which
would have the six winning numbers. We do this by calculating the combinations
possible of six numbers from a choice of 49 numbers. By using the Excel combination
formula I determined this number to be 13,983,816 possible combinations. Since there is
one way to win, the probability of winning the first prize is 1/13,983,816.
The next step is to calculate how many different combinations there are to obtain
a winning ticket for the second prize. This is accomplished by determining the
combination of five out of six correct numbers ( 6 ), and multiply this by the
combination of one out of the remaining 43 numbers ( 43 ), the total of which is 258.
The probability of winning the second prize is therefore 43/2330636.