# Maths question - I'm confused

#### Irvin

##### Member

I have posted a thread in the lotto tool box section trying to reinvent the wheel.

But I am having a problem with the maths side and here is the question;

If you have a ticket where each line has 6 numbers on it. How many line combinations can you get from the following;

Group A has 4 numbers (1,2,3,4).

Group B has 4 numbers (5,6,7,8).

Group C has 3 numbers (9,10,11).

Group D has 3 numbers (12,13,14).

You must use all the numbers from each group with the minimum from each group being 0 and the max is 2.

Correct answer is worth 10 points (You have to persuade me though because I dont know it)

Correct answer with full workings is worth 100 points.

Good luck and you have 1 hour starting from now.

#### Nick Koutras

##### Member
The only good combinations from each group that sum up to 6 are:

case 1: 0222
case 2: 1122

Expanding the above:
Case 1:

ABCD
0222 =1*4c2*3c2*3c2=1*6*3*3
2022 =4c2*1*3c3*3c2=6*1*3*3
2202 =4c2*4c2*1*3c2=6*6*1*3
2220 =4c2*4c2*3c3*1=6*6*3*1

=54+54+108+108=324

Case 2:

ABCD
1122=4c1*4c1*3c2*3c2
1212=4c1*4c2*3c1*3c2
1221=4c1*4c2*3c2*3c1
2112=4c2*4c1*3c1*3c2
2121=4c2*4c1*3c2*3c1
2211=4c2*4c2*3c1*3c1

=144+216+216+216+216+324=1080

So the (324+1080)=1404 combinations
out of the 14c6=3003 comply to

#### Irvin

##### Member
Nick,

Thanks for that.

Knew you would figure this one out.

Regards,

Irvin

#### Snides

##### Member
Nick Koutras said:

=54+54+108+108=324

=144+216+216+216+216+324=1080

So the (324+1080)=1404 combinations
out of the 14c6=3003 comply to