Euromillions Odds

It is the European draw that distributes the largest prizes, reaching jackpots of up to 190 million euros in some draws, but this means that this draw has to have an added complication: the enormous number of possible combinations.

The game consists of matching 5 numbers from a table of 50 (from 1 to 50) and also matching 2 numbers (stars) from a table of 12 (from 1 to 12). In other words, to be eligible for the first prize you must match 7 numbers (5 + 2).
Drawings are held ontes y viernes con un único sorteo cada día para todos los países que participan: Francia, Reino Unido, Austria, Bélgica, Irlanda, Luxemburgo, Portugal y Suiza y España. El precio de cada apuesta es de 2,50 euros.

In Euromillions, 50% of the proceeds are destined to prizes, distributed among 13 prize categories.

The probability of matching the first category (5 numbers and 2 stars) is almost 1 in 140 million, although fortunately there are many more categories of prizes in which you can match and get a good prize

Table of hit probabilities in each category (numbers + stars):

Category	Probabilities of success
1ª Category (5+2)	1 among 139.838.160
2ª Category (5+1)	1 among 6.991.908
3ª Category (5+0)	1 among 3.107.515
4ª Category (4+2)	1 among 621.503
5ª Category (4+1)	1 among 31.075
6ª Category (3+2)	1 among 14,125
7ª Category (4+0)	1 among 13.811
8ª Category (2+2)	1 among 985
9ª Category (3+1)	1 among 706
10ª Category (3+0)	1 among 314
11ª Category (1+2)	1 among 188
12ª Category (2+1)	1 among 49
13ª Category (2+0)	1 among 22

The probability in a multiple combination of 10 Euromillions numbers of matching 5, 4, 3, 2, 1, 0.
It would be as follows:

Assuming 1° that the probability of matching 5 numbers out of the 50 that there are:

c(50,5)= 2.118.760 --->1/2.118.760........0.0000471 %
X=Multiple bets,Y=Y=Successes sought C(X,Y)*C(50-X,5-Y) --->these would be the favorable cases.

5 Hits (10 MULTIPLES, 5 HITS) = C(10,5)*C(50-10,5-5)= 252
4 Hits (10 MULTIPLES, 4 HITS) = C(10,4)*C(50-10,5-4)= 8.400
3 Hits (10 MULTIPLES, 3 HITS) = C(10,3)*C(50-10,5-3)= 93.600
2 Hits (10 MULTIPLES, 2 HITS) = C(10,2)*C(50-10,5-2)= 444.600
1 hits (10 MULTIPLES, 1 HITS) = C(10,1)*C(50-10,5-1)= 913.900
0 hits (10 MULTIPLES, 0 HITS) = C(10,0)*C(50-10,5-0)= 658.008

Therefore, the probability of 5, 4, 3, 2, 1 and 0 successes would be as follows:

5: 252/2.118.760 ---> 0,012%
4: 8.400/2.118.760 ---> 0,4%
3: 93.600/2.118.760 ---> 4,4 %
2: 444.600/2.118.760 ---> 21 %
1: 913.900/2.118.760 ---> 43 %
0: 658.008/2.118.760 ---> 31 %