# binomial theorem in lotto

#### Matrix

##### Member
I want to provide a idea about binomial theorem in lotto here.

For example, there are 861 pairs combinations in 6/42. And there are 15 paies comb. every draw. If we can exactly caculate what's the values of theory and what's the values of reallity, we can easily to calute the difference between both of them(T&R). Then, I can use this data to predict what's pair numbers have highly probability to appear in next draw.

#### GillesD

##### Member
Pairs in a 6/42 lottery

This is what I calculate:

For a 6/42 lottery:
In the 5,245,786 combinations, each of the possible 861 pairs (from 1,2 to 41,42) would occur 91,390 times.
This would give a probability of 91,390/(5,245,786x15) or 0.116144% (rounded to the 6th decimal).

For a 6/49 lottery:
In the 13,983,816 combinations, each of the possible 1176 pairs (from 1,2 to 48,49) would occur 178,365 times.
This would give a probability of 178,365/(13,983,816x15) or 0.085034% (rounded to the 6th decimal).

I am pretty sure of these values but if somebody can confirm them, I would appreciate.

#### Nick Koutras

##### Member
Use the XL function BINOMDIST

or use LottoStatisticsXL to display
the 2-plets for the duration you are using
then follow the 3 steps below

Step 1: in cell J3 enter Duration
Step 2 :in cell K3 enter =15/1176 , Probability
Step 3: Copy formula to cells C4--> max Frq
=BINOMDIST(A4,\$J\$3,\$K\$3,FALSE)*1176

Now beside the Colunm Qty you have the
Theoretical Distribution of the 2plets for the duration you desire.

Conclusions are up to you.

#### Matrix

##### Member
Well done, GD and nick!!! 