5 Main Numbers (Jackpot)

1 in 2,118,760.000 
Show/Hide › 
The odds for this prize level are not influenced by any 'Bonus Balls' and only the variables associated with the main ball pool are required to calculate the correct odds. The following formula is therefore used (Please note: calculations have been rounded): 

C(n,r) = Odds of correctly choosing r balls from n
n = Number of balls in the main pool
r = Balls drawn from the main pool
m = Balls to be matched from the main pool


Substitute:
n for 50 (number of balls in the main pool)
r for 5 (balls drawn from the main pool)
m for 5 (balls to be matched from the main pool)


Expand:
C(50,5) = 50! ÷ (5! × (505)!)
C(5,5) = 5! ÷ (5! × (55)!)
C(505,55) = 45! ÷ (0! × (450)!)
! means 'Factorial' eg: 50! = 50 × 49 × 48 ... × 1
Note: 0! = 1


Simplify:
50! ÷ (5! × (505)!) = 2,118,760
5! ÷ (5! × (55)!) = 1
45! ÷ (0! × (450)!) = 1

2,118,760 
= 
2,118,760.000 
1 

Calculate:
2,118,760 ÷ (1 × 1) = 2,118,760.000


4 Main Numbers + Bonus Ball

1 in 423,752.000 
Show/Hide › 
The odds for this prize level are directly influenced by the Bonus Ball. Since the Bonus Ball is drawn from the same pool as the main numbers, the following formula is used (Please note: calculations have been rounded):

C(n,r) 

× 
C(r,m) 
× 
C(nr,rm) 

C(n,r) = Odds of correctly choosing r balls from n
n = Number of balls in the main pool
r = Balls drawn from the main pool
m = Balls to be matched from the main pool

C(50,5) 

× 
C(5,4) 
× 
C(505,54) 

Substitute:
n for 50 (number of balls in the main pool)
r for 5 (balls drawn from the main pool)
m for 4 (balls to be matched from the main pool)


Expand:
C(50,5) = 50! ÷ (5! × (505)!)
C(5,4) = 5! ÷ (4! × (54)!)
C(505,54) = 45! ÷ (1! × (451)!)
! means 'Factorial' eg: 50! = 50 × 49 × 48 ... × 1
Note: 0! = 1

2,118,760 
0.0222 
× 
5 
× 
45 

Simplify:
50! ÷ (5! × (505)!) = 2,118,760
(54) ÷ (505) = 0.0222
5! ÷ (4! × (54)!) = 5
45! ÷ (1! × (451)!) = 45

2,118,760 
= 
423,752.000 
5 

Calculate:
2,118,760 ÷ (0.0222 × 5 × 45) = 423,752.000


4 Main Numbers

1 in 9,630.727 
Show/Hide › 
The odds for this prize level are indirectly influenced by the Bonus Ball. Even though this prize level only involves matching 4 main numbers, the fact that you can also match 4 main numbers and a Bonus Ball means the odds of matching 4 main numbers alone are increased. Since the Bonus Ball is also drawn from the same pool as the main numbers, the following formula is used (Please note: calculations have been rounded):

C(n,r) 

× 
C(r,m) 
× 
C(nr,rm) 

C(n,r) = Odds of correctly choosing r balls from n
n = Number of balls in the main pool
r = Balls drawn from the main pool
m = Balls to be matched from the main pool

C(50,5) 

× 
C(5,4) 
× 
C(505,54) 

Substitute:
n for 50 (number of balls in the main pool)
r for 5 (balls drawn from the main pool)
m for 4 (balls to be matched from the main pool)


Expand:
C(50,5) = 50! ÷ (5! × (505)!)
C(5,4) = 5! ÷ (4! × (54)!)
C(505,54) = 45! ÷ (1! × (451)!)
! means 'Factorial' eg: 50! = 50 × 49 × 48 ... × 1
Note: 0! = 1

2,118,760 
0.9778 
× 
5 
× 
45 

Simplify:
50! ÷ (5! × (505)!) = 2,118,760
(5055+4) ÷ (505) = 0.0222
5! ÷ (4! × (54)!) = 5
45! ÷ (1! × (451)!) = 45

2,118,760 
= 
9,630.727 
220 

Calculate:
2,118,760 ÷ (0.9778 × 5 × 45) = 9,630.727


3 Main Numbers + Bonus Ball

1 in 4,815.364 
Show/Hide › 
The odds for this prize level are directly influenced by the Bonus Ball. Since the Bonus Ball is drawn from the same pool as the main numbers, the following formula is used (Please note: calculations have been rounded):

C(n,r) 

× 
C(r,m) 
× 
C(nr,rm) 

C(n,r) = Odds of correctly choosing r balls from n
n = Number of balls in the main pool
r = Balls drawn from the main pool
m = Balls to be matched from the main pool

C(50,5) 

× 
C(5,3) 
× 
C(505,53) 

Substitute:
n for 50 (number of balls in the main pool)
r for 5 (balls drawn from the main pool)
m for 3 (balls to be matched from the main pool)


Expand:
C(50,5) = 50! ÷ (5! × (505)!)
C(5,3) = 5! ÷ (3! × (53)!)
C(505,53) = 45! ÷ (2! × (452)!)
! means 'Factorial' eg: 50! = 50 × 49 × 48 ... × 1
Note: 0! = 1

2,118,760 
0.0444 
× 
10 
× 
990 

Simplify:
50! ÷ (5! × (505)!) = 2,118,760
(53) ÷ (505) = 0.0444
5! ÷ (3! × (53)!) = 10
45! ÷ (2! × (452)!) = 990

2,118,760 
= 
4,815.364 
440 

Calculate:
2,118,760 ÷ (0.0444 × 10 × 990) = 4,815.364


3 Main Numbers

1 in 223.970 
Show/Hide › 
The odds for this prize level are indirectly influenced by the Bonus Ball. Even though this prize level only involves matching 3 main numbers, the fact that you can also match 3 main numbers and a Bonus Ball means the odds of matching 3 main numbers alone are increased. Since the Bonus Ball is also drawn from the same pool as the main numbers, the following formula is used (Please note: calculations have been rounded):

C(n,r) 

× 
C(r,m) 
× 
C(nr,rm) 

C(n,r) = Odds of correctly choosing r balls from n
n = Number of balls in the main pool
r = Balls drawn from the main pool
m = Balls to be matched from the main pool

C(50,5) 

× 
C(5,3) 
× 
C(505,53) 

Substitute:
n for 50 (number of balls in the main pool)
r for 5 (balls drawn from the main pool)
m for 3 (balls to be matched from the main pool)


Expand:
C(50,5) = 50! ÷ (5! × (505)!)
C(5,3) = 5! ÷ (3! × (53)!)
C(505,53) = 45! ÷ (2! × (452)!)
! means 'Factorial' eg: 50! = 50 × 49 × 48 ... × 1
Note: 0! = 1

2,118,760 
0.9556 
× 
10 
× 
990 

Simplify:
50! ÷ (5! × (505)!) = 2,118,760
(5055+3) ÷ (505) = 0.0444
5! ÷ (3! × (53)!) = 10
45! ÷ (2! × (452)!) = 990

2,118,760 
= 
223.970 
9,460 

Calculate:
2,118,760 ÷ (0.9556 × 10 × 990) = 223.970


2 Main Numbers + Bonus Ball

1 in 223.970 
Show/Hide › 
The odds for this prize level are directly influenced by the Bonus Ball. Since the Bonus Ball is drawn from the same pool as the main numbers, the following formula is used (Please note: calculations have been rounded):

C(n,r) 

× 
C(r,m) 
× 
C(nr,rm) 

C(n,r) = Odds of correctly choosing r balls from n
n = Number of balls in the main pool
r = Balls drawn from the main pool
m = Balls to be matched from the main pool

C(50,5) 

× 
C(5,2) 
× 
C(505,52) 

Substitute:
n for 50 (number of balls in the main pool)
r for 5 (balls drawn from the main pool)
m for 2 (balls to be matched from the main pool)


Expand:
C(50,5) = 50! ÷ (5! × (505)!)
C(5,2) = 5! ÷ (2! × (52)!)
C(505,52) = 45! ÷ (3! × (453)!)
! means 'Factorial' eg: 50! = 50 × 49 × 48 ... × 1
Note: 0! = 1

2,118,760 
0.0667 
× 
10 
× 
14,190 

Simplify:
50! ÷ (5! × (505)!) = 2,118,760
(52) ÷ (505) = 0.0667
5! ÷ (2! × (52)!) = 10
45! ÷ (3! × (453)!) = 14,190

2,118,760 
= 
223.970 
9,460 

Calculate:
2,118,760 ÷ (0.0667 × 10 × 14,190) = 223.970


Overall Odds: 1 in 108.177 