Answer to the Problem of the Week
for the week of May 22, 2006

Virginia LOTTO South

In the Virginia LOTTO South game, participants select six numbers from 1 to 49. You win a prize if you can match 3, 4, 5, or 6 numbers.

What is the probability that a person would match none of the numbers?
Answers must be expressed as a decimal (correct to four decimal places like .xxxx), a percent (correct to 2 decimal places like xx.xx%), or in the form "1 in xx.xx" (correct to 2 decimal places).

Side note:
On the day that I turned in my resignation to my superintendent, I decided to purchase a Lotto South ticket.   I don't normally purchase lottery tickets; in fact, I believe that the lottery is a tax on people who are bad at math.   But I thought that this would make a great story line -- "After 38 years of teaching, Handley Math Teacher wins lotto on the day he retires."   Well, it didn't happen; and in fact, I matched no numbers!   I think that God was trying to tell me something there.   Hence, this week's problem!   And, yes, this will the final Problem of the Week for awhile.   After living my first 60 years in Virginia, my wife and I are moving to Colorado for our next 60 years.   I plan to post a Problem of the Month starting in January 2007.   Thanks to all who have sent in your answers over the years -- it's been great!   I have posted a "Problem of the Week" every week in my classroom since September 1968, and I have posted one on the internet since March 1998.   So, this is going to leave a void in my life.   Don't forget -- you can work on some of the past problems that have been posted on the Handley Math Page by clicking below:  
List of Problems of the Week


 

Solution to the Problem:

The answer is .4360 or 43.60% or 1 in 2.29 that a person would match no numbers!

First, determine the number of different combinations of 49 numbers taken 6 at a time.   There are 13,983,816 different possible combinations.   So, the chances of matching all six numbers are 1 in 13,983,816.
Next, you must figure the number of ways in which none of the numbers matched.   There are 43 numbers which do not match, so take the number of combinations of 43 numbers taken 6 at a time.   This answer is 6,096,454.   Now, divide these two numbers to get your answer.   The probability of not matching any of the six numbers is 6,096,454 divided by 13,983,816.


Correctly solved by:

1. Leon Litvachuk Manual Arts High School
Los Angeles, California
2. Sagar Patel Brookstone School
Columbus, Georgia
3. Jim Arrison Norristown, Pennsylvania
4. Richard Johnson La Jolla, California
5. Larry Schwartz Norwalk, Connecticut
6. Ibraheem Rasoul Harrionburg High school
Harrionburg, Virginia
7. Ben Bassett Washington Township High School
Sewell, New Jersey
8. Ben Reedy ----------
9. Nathan Hissong Mountain View High School
Mountain View, Wyoming
10. Paul Verschueren Seattle, Washington
11. Lucas Woodbury Mountain View High School
Mountain View, Wyoming
12. Lauren Coles Chelmsford High School
Chelmsford, Massachussetts