Lottery math with four-function calculator

by Bavi_H, 6/10/2009

After reading about lottery mathematics, I noticed a pattern you can use to calculate the number of ways to match every possible number of balls, where each result is built up from the previous result. You can memorize the steps and preform them with a pencil, paper, and a basic four-function calculator.

Here's an example for Lotto Texas, in which you choose 6 numbers out of 54.

1 M+	1	ways to match 6
÷ 1 ÷ 1 × 6 × 48 = M+	288	ways to match 5
÷ 2 ÷ 2 × 5 × 47 = M+	16920	ways to match 4
÷ 3 ÷ 3 × 4 × 46 = M+	345920	ways to match 3
÷ 4 ÷ 4 × 3 × 45 = M+	2918700	ways to match 2
÷ 5 ÷ 5 × 2 × 44 = M+	10273824	ways to match 1
÷ 6 ÷ 6 × 1 × 43 = M+	12271512	ways to match 0
MR	25827165	total combinations

Here's how to remember the steps.

• The first line has a 1.
• The remaining lines use the following pattern:
  • The first and second columns go from 1 up to the number of balls drawn.
  • The third column goes from the number of balls drawn down to 1.
  • The fourth column goes from the number of balls not drawn downward.

When you want to do a calculation, you can write out the entire calculation pattern on a piece of paper. Then you can enter the sequence on a calculator, and write down the results at the end of each line.

Links

Lottery mathematics from Wikipedia
en.wikipedia.org/wiki/Lottery_mathematics

How to Play Lotto Texas from Texas Lottery Commission
www.txlottery.org/export/sites/lottery/Games/Lotto_Texas/How_to_Play_Lotto_Texas.html