Winning the lottery is the dream of many Brazilian players, who seek out lottery outlets to bet on Caixa Econômica Federal lotteries. The most awaited moment is the drawing of numbers that will decide if there will be winners. The most desired by all is the Mega-Sena, your card is composed of 60 numbers, from 1 to 60. The minimum bet in this lottery consists of six numbers and the maximum of fifteen, but the bet amounts vary according to the increase in numbers bet, as the more numbers dialed, the greater the chance of to win. The accumulated draws have already offered prizes equivalent to R$300 million to the winner.
In the rounds, six numbers are drawn out of the sixty, and cash prizes are paid to whoever hits four (square), five (quin) or six (sena) numbers. The amount of money paid to hitters on the court and corner are proportional to the amounts collected in the contest. Millionaire prizes are only paid to those who match the six drawn numbers. If the number of winners is greater than one, the prize is divided into equal parts. But
what is the chance of a person winning by playing just one card filled with six numbers?
The dream of becoming a millionaire makes many Brazilians bet on the Mega-Sena.
What are the chances of getting the Mega-Sena numbers right?
The chances of hitting the six numbers are calculated using a simple combination of sixty elements taken from six to six, C60,6. The possible numbers of combinations are calculated according to the following mathematical expression:
Çno, p = no!
p!(n - p)!
Remembering that simple combinations are groups of distinct elements that differ from each other by the nature of the elements. In calculations involving combinations, we use the factorial of a natural number that consists of multiplying this number by all its predecessors up to the number one, for example:4! = 4*3*2*1 = 24.
This way, let's calculate the possible combinations existing in Mega Sena:
Ç60,6 = 60! ⇒ 60! ⇒ 60*59*58*57*56*55*54! ⇒
6!(60 - 6)! 6!54! 6!54!
Ç60,6 = 60*59*58*57*56*55 ⇒
6*5*4*3*2*1
Ç60,6 = 36.045.979.200 ⇒ 50.063.860
720
There are 50,063,860 (fifty million sixty three thousand eight hundred and sixty) different ways to choose the six numbers from 1 to 60. Here are some possible combinations:
01 – 02 – 03 – 04 – 05 – 06
01 – 02 – 03 – 04 – 05 – 07
01 – 02 – 03 – 04 – 05 – 08
01 – 02 – 03 – 04 – 05 – 09
01 – 02 – 03 – 04 – 05 – 10
01 – 03 – 04 – 05 – 15 – 16
12 – 14 – 25 – 32 – 48 – 55
09 – 12 – 24 – 37 – 55 – 58
02 – 31 – 36 – 42 – 46 – 57
08 – 10 – 15 – 21 – 32 – 38
09 – 18 – 27 – 31 – 40 – 50
02 – 07 – 12 – 18 – 24 – 30
19 – 23 – 27 – 30 – 38 – 42
12 – 15 – 35 – 42 – 49 – 51
03 – 06 – 12 – 22 – 28 – 46
14 – 19 – 23 – 36 – 39 – 53
The chances of a person hitting just one single card is 1 in 50,063,860, this corresponds to 1/50,063,860 = 0.00000002 which corresponds to 0.000002%.
*Image credit: Gabriel_Ramos | Shutterstock
by Mark Noah
Graduated in Mathematics
Source: Brazil School - https://brasilescola.uol.com.br/matematica/chances-ganhar-na-mega-sena.htm