6 Main Numbers (Jackpot)

1 in 10,737,573.000 
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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 47 (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(47,6) = 47! ÷ (6! × (476)!)
C(6,6) = 6! ÷ (6! × (66)!)
C(476,66) = 41! ÷ (0! × (410)!)
! means 'Factorial' eg: 47! = 47 × 46 × 45 ... × 1
Note: 0! = 1


Simplify:
47! ÷ (6! × (476)!) = 10,737,573
6! ÷ (6! × (66)!) = 1
41! ÷ (0! × (410)!) = 1

10,737,573 
= 
10,737,573.000 
1 

Calculate:
10,737,573 ÷ (1 × 1) = 10,737,573.000


5 Main Numbers + Bonus Ball

1 in 1,789,595.500 
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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(47,6) 

× 
C(6,5) 
× 
C(476,65) 

Substitute:
n for 47 (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(47,6) = 47! ÷ (6! × (476)!)
C(6,5) = 6! ÷ (5! × (65)!)
C(476,65) = 41! ÷ (1! × (411)!)
! means 'Factorial' eg: 47! = 47 × 46 × 45 ... × 1
Note: 0! = 1

10,737,573 
0.0244 
× 
6 
× 
41 

Simplify:
47! ÷ (6! × (476)!) = 10,737,573
(65) ÷ (476) = 0.0244
6! ÷ (5! × (65)!) = 6
41! ÷ (1! × (411)!) = 41

10,737,573 
= 
1,789,595.500 
6 

Calculate:
10,737,573 ÷ (0.0244 × 6 × 41) = 1,789,595.500


5 Main Numbers

1 in 44,739.888 
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The odds for this prize level are indirectly influenced by the Bonus Ball. Even though this prize level only involves matching 5 main numbers, the fact that you can also match 5 main numbers and a Bonus Ball means the odds of matching 5 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(47,6) 

× 
C(6,5) 
× 
C(476,65) 

Substitute:
n for 47 (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(47,6) = 47! ÷ (6! × (476)!)
C(6,5) = 6! ÷ (5! × (65)!)
C(476,65) = 41! ÷ (1! × (411)!)
! means 'Factorial' eg: 47! = 47 × 46 × 45 ... × 1
Note: 0! = 1

10,737,573 
0.9756 
× 
6 
× 
41 

Simplify:
47! ÷ (6! × (476)!) = 10,737,573
(4766+5) ÷ (476) = 0.0244
6! ÷ (5! × (65)!) = 6
41! ÷ (1! × (411)!) = 41

10,737,573 
= 
44,739.888 
240 

Calculate:
10,737,573 ÷ (0.9756 × 6 × 41) = 44,739.888


4 Main Numbers + Bonus Ball

1 in 17,895.955 
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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(47,6) 

× 
C(6,4) 
× 
C(476,64) 

Substitute:
n for 47 (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(47,6) = 47! ÷ (6! × (476)!)
C(6,4) = 6! ÷ (4! × (64)!)
C(476,64) = 41! ÷ (2! × (412)!)
! means 'Factorial' eg: 47! = 47 × 46 × 45 ... × 1
Note: 0! = 1

10,737,573 
0.0488 
× 
15 
× 
820 

Simplify:
47! ÷ (6! × (476)!) = 10,737,573
(64) ÷ (476) = 0.0488
6! ÷ (4! × (64)!) = 15
41! ÷ (2! × (412)!) = 820

10,737,573 
= 
17,895.955 
600 

Calculate:
10,737,573 ÷ (0.0488 × 15 × 820) = 17,895.955


4 Main Numbers

1 in 917.741 
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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(47,6) 

× 
C(6,4) 
× 
C(476,64) 

Substitute:
n for 47 (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(47,6) = 47! ÷ (6! × (476)!)
C(6,4) = 6! ÷ (4! × (64)!)
C(476,64) = 41! ÷ (2! × (412)!)
! means 'Factorial' eg: 47! = 47 × 46 × 45 ... × 1
Note: 0! = 1

10,737,573 
0.9512 
× 
15 
× 
820 

Simplify:
47! ÷ (6! × (476)!) = 10,737,573
(4766+4) ÷ (476) = 0.0488
6! ÷ (4! × (64)!) = 15
41! ÷ (2! × (412)!) = 820

10,737,573 
= 
917.741 
11,700 

Calculate:
10,737,573 ÷ (0.9512 × 15 × 820) = 917.741


3 Main Numbers + Bonus Ball

1 in 688.306 
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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(47,6) 

× 
C(6,3) 
× 
C(476,63) 

Substitute:
n for 47 (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(47,6) = 47! ÷ (6! × (476)!)
C(6,3) = 6! ÷ (3! × (63)!)
C(476,63) = 41! ÷ (3! × (413)!)
! means 'Factorial' eg: 47! = 47 × 46 × 45 ... × 1
Note: 0! = 1

10,737,573 
0.0732 
× 
20 
× 
10,660 

Simplify:
47! ÷ (6! × (476)!) = 10,737,573
(63) ÷ (476) = 0.0732
6! ÷ (3! × (63)!) = 20
41! ÷ (3! × (413)!) = 10,660

10,737,573 
= 
688.306 
15,600 

Calculate:
10,737,573 ÷ (0.0732 × 20 × 10,660) = 688.306


3 Main Numbers

1 in 54.340 
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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(47,6) 

× 
C(6,3) 
× 
C(476,63) 

Substitute:
n for 47 (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(47,6) = 47! ÷ (6! × (476)!)
C(6,3) = 6! ÷ (3! × (63)!)
C(476,63) = 41! ÷ (3! × (413)!)
! means 'Factorial' eg: 47! = 47 × 46 × 45 ... × 1
Note: 0! = 1

10,737,573 
0.9268 
× 
20 
× 
10,660 

Simplify:
47! ÷ (6! × (476)!) = 10,737,573
(4766+3) ÷ (476) = 0.0732
6! ÷ (3! × (63)!) = 20
41! ÷ (3! × (413)!) = 10,660

10,737,573 
= 
54.340 
197,600 

Calculate:
10,737,573 ÷ (0.9268 × 20 × 10,660) = 54.340


2 Main Numbers + Bonus Ball

1 in 72.453 
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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(47,6) 

× 
C(6,2) 
× 
C(476,62) 

Substitute:
n for 47 (number of balls in the main pool)
r for 6 (balls drawn from the main pool)
m for 2 (balls to be matched from the main pool)


Expand:
C(47,6) = 47! ÷ (6! × (476)!)
C(6,2) = 6! ÷ (2! × (62)!)
C(476,62) = 41! ÷ (4! × (414)!)
! means 'Factorial' eg: 47! = 47 × 46 × 45 ... × 1
Note: 0! = 1

10,737,573 
0.0976 
× 
15 
× 
101,270 

Simplify:
47! ÷ (6! × (476)!) = 10,737,573
(62) ÷ (476) = 0.0976
6! ÷ (2! × (62)!) = 15
41! ÷ (4! × (414)!) = 101,270

10,737,573 
= 
72.453 
148,200 

Calculate:
10,737,573 ÷ (0.0976 × 15 × 101,270) = 72.453


Overall Odds: 1 in 28.714 