6 Main Numbers (Jackpot)

1 in 622,614,630.000 
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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 90 (number of balls in the main pool)
r for 6 (balls drawn from the main pool)
m for 6 (balls to be matched from the main pool)


Expand:
C(90,6) = 90! ÷ (6! × (906)!)
C(6,6) = 6! ÷ (6! × (66)!)
C(906,66) = 84! ÷ (0! × (840)!)
! means 'Factorial' eg: 90! = 90 × 89 × 88 ... × 1
Note: 0! = 1


Simplify:
90! ÷ (6! × (906)!) = 622,614,630
6! ÷ (6! × (66)!) = 1
84! ÷ (0! × (840)!) = 1

622,614,630 
= 
622,614,630.000 
1 

Calculate:
622,614,630 ÷ (1 × 1) = 622,614,630.000


5 Main Numbers + Jolly Ball

1 in 103,769,105.000 
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The odds for this prize level are directly influenced by the Jolly Ball. Since the Jolly 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(90,6) 

× 
C(6,5) 
× 
C(906,65) 

Substitute:
n for 90 (number of balls in the main pool)
r for 6 (balls drawn from the main pool)
m for 5 (balls to be matched from the main pool)


Expand:
C(90,6) = 90! ÷ (6! × (906)!)
C(6,5) = 6! ÷ (5! × (65)!)
C(906,65) = 84! ÷ (1! × (841)!)
! means 'Factorial' eg: 90! = 90 × 89 × 88 ... × 1
Note: 0! = 1

622,614,630 
0.0119 
× 
6 
× 
84 

Simplify:
90! ÷ (6! × (906)!) = 622,614,630
(65) ÷ (906) = 0.0119
6! ÷ (5! × (65)!) = 6
84! ÷ (1! × (841)!) = 84

622,614,630 
= 
103,769,105.000 
6 

Calculate:
622,614,630 ÷ (0.0119 × 6 × 84) = 103,769,105.000


5 Main Numbers

1 in 1,250,230.181 
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The odds for this prize level are indirectly influenced by the Jolly Ball. Even though this prize level only involves matching 5 main numbers, the fact that you can also match 5 main numbers and a Jolly Ball means the odds of matching 5 main numbers alone are increased. Since the Jolly 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(90,6) 

× 
C(6,5) 
× 
C(906,65) 

Substitute:
n for 90 (number of balls in the main pool)
r for 6 (balls drawn from the main pool)
m for 5 (balls to be matched from the main pool)


Expand:
C(90,6) = 90! ÷ (6! × (906)!)
C(6,5) = 6! ÷ (5! × (65)!)
C(906,65) = 84! ÷ (1! × (841)!)
! means 'Factorial' eg: 90! = 90 × 89 × 88 ... × 1
Note: 0! = 1

622,614,630 
0.9881 
× 
6 
× 
84 

Simplify:
90! ÷ (6! × (906)!) = 622,614,630
(9066+5) ÷ (906) = 0.0119
6! ÷ (5! × (65)!) = 6
84! ÷ (1! × (841)!) = 84

622,614,630 
= 
1,250,230.181 
498 

Calculate:
622,614,630 ÷ (0.9881 × 6 × 84) = 1,250,230.181


4 Main Numbers

1 in 11,906.954 
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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 90 (number of balls in the main pool)
r for 6 (balls drawn from the main pool)
m for 4 (balls to be matched from the main pool)


Expand:
C(90,6) = 90! ÷ (6! × (906)!)
C(6,4) = 6! ÷ (4! × (64)!)
C(906,64) = 84! ÷ (2! × (842)!)
! means 'Factorial' eg: 90! = 90 × 89 × 88 ... × 1
Note: 0! = 1


Simplify:
90! ÷ (6! × (906)!) = 622,614,630
6! ÷ (4! × (64)!) = 15
84! ÷ (2! × (842)!) = 3,486

622,614,630 
= 
11,906.954 
52,290 

Calculate:
622,614,630 ÷ (15 × 3,486) = 11,906.954


3 Main Numbers

1 in 326.715 
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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 90 (number of balls in the main pool)
r for 6 (balls drawn from the main pool)
m for 3 (balls to be matched from the main pool)


Expand:
C(90,6) = 90! ÷ (6! × (906)!)
C(6,3) = 6! ÷ (3! × (63)!)
C(906,63) = 84! ÷ (3! × (843)!)
! means 'Factorial' eg: 90! = 90 × 89 × 88 ... × 1
Note: 0! = 1


Simplify:
90! ÷ (6! × (906)!) = 622,614,630
6! ÷ (3! × (63)!) = 20
84! ÷ (3! × (843)!) = 95,284

622,614,630 
= 
326.715 
1,905,680 

Calculate:
622,614,630 ÷ (20 × 95,284) = 326.715


Overall Odds: 1 in 317.908 