Possible Combinations with Restricted Selections

Could someone help me with this:

There are 32 selections seeded from 1 to 4 into 8 groups (i.e. group A

has a 1, 2, 3 & 4 seed, group 2 has an 1, 2, 3 & 4 seed etc). I have to pick 8 of

these, 1 (and only 1) from each group and can only pick 2 seed 1s, 2 seed 2s, 2 seed 3s and
2 seed 4s.

This may help explain it better:

One valid selection might be A1, B2, C3, D4, E1, F2, G3, H4 while another is A4, B3, C2, D1, E4,
F3, G2, H1

However A1 and A2 cannot be selected together nor A1, B1 and C1.

The whole list is:

G S

-- ---

A 1

A 2

A 3

A 4

B 1

B 2

B 3

B 4

C 1

C 2

C 3

C 4

D 1

D 2

D 3

D 4

E 1

E 2

E 3

E 4

F 1

F 2

F 3

F 4

G 1

G 2

G 3

G 4

H 1

H 2

H 3

H 4

I am trying to find out how many unique combinations there are from this.

It would be nice to know how you work it out too.

I think that due to the restrictions there are only 107 possible combinations, but I could easily be
well wrong as my math is not that great.

Also I am interested to know how changing the rules to only having to pick four selections where I
must pick 1 of each seed but can pick the four from any group as long as I only pick at most 1 from
each group would effect the possible combinations, I imagine this will increase the possible
selections by a lot.

Thank you for getting this far

Reply 1

Unregistered

Well imagine that the selectors wish to indicate to the players which have been picked to play.
Suppose that you have 8 boxes labelled A to H and 8 cards 2 of 1, 2 of 2, 2 of 3 and 2 of 4 What the
selectors have to do is place the 8 cards in the eight boxes and they can do this in any order.

This can be done in 8! / 2^4 ways = 2520 ways, many more than the 107 you thought possible I shall
give you the first 6.

A B C D E F G H 1 1 2 2 3 3 4 4 1 1 2 2 3 4 3 4 1 1 2 2 3 4 4 3 1 1 2 2 4 3 3 4 1 1 2 2 4 3 4 3 1 1
2 2 4 4 3 3

As to your second question You can pick a number 1 seed from one of 8 groups Then the 2nd seed from
one of the remaining 7 groups 3rd seed from one of the remaining 6 groups 4th seed from one of the
remaining 5 groups.

So you can make your choice in 8x7x6x5 different ways = 1680 ways

Joe Bradley

Michael Darling wrote in message ...
[q1]>Could someone help me with this:[/q1]
[q1]>[/q1]
[q1]>There are 32 selections seeded from 1 to 4 into 8 groups (i.e. group A[/q1]
[q1]>[/q1]
[q1]>has a 1, 2, 3 & 4 seed, group 2 has an 1, 2, 3 & 4 seed etc). I have to[/q1]
pick
[q1]>8 of[/q1]
[q1]>[/q1]
[q1]> these, 1 (and only 1) from each group and can only pick 2 seed 1s, 2 seed 2s, 2 seed 3s and 2[/q1]
[q1]> seed 4s.[/q1]
[q1]>[/q1]
[q1]>This may help explain it better:[/q1]
[q1]>[/q1]
[q1]> One valid selection might be A1, B2, C3, D4, E1, F2, G3, H4 while another is A4, B3, C2, D1, E4,[/q1]
[q1]> F3, G2, H1[/q1]
[q1]>[/q1]
[q1]>However A1 and A2 cannot be selected together nor A1, B1 and C1.[/q1]
[q1]>[/q1]
[q1]>The whole list is:[/q1]
[q1]>[/q1]
[q1]>G S[/q1]
[q1]>[/q1]
[q1]>-- ---[/q1]
[q1]>[/q1]
[q1]>A 1[/q1]
[q1]>[/q1]
[q1]>A 2[/q1]
[q1]>[/q1]
[q1]>A 3[/q1]
[q1]>[/q1]
[q1]>A 4[/q1]
[q1]>[/q1]
[q1]>B 1[/q1]
[q1]>[/q1]
[q1]>B 2[/q1]
[q1]>[/q1]
[q1]>B 3[/q1]
[q1]>[/q1]
[q1]>B 4[/q1]
[q1]>[/q1]
[q1]>C 1[/q1]
[q1]>[/q1]
[q1]>C 2[/q1]
[q1]>[/q1]
[q1]>C 3[/q1]
[q1]>[/q1]
[q1]>C 4[/q1]
[q1]>[/q1]
[q1]>D 1[/q1]
[q1]>[/q1]
[q1]>D 2[/q1]
[q1]>[/q1]
[q1]>D 3[/q1]
[q1]>[/q1]
[q1]>D 4[/q1]
[q1]>[/q1]
[q1]>E 1[/q1]
[q1]>[/q1]
[q1]>E 2[/q1]
[q1]>[/q1]
[q1]>E 3[/q1]
[q1]>[/q1]
[q1]>E 4[/q1]
[q1]>[/q1]
[q1]>F 1[/q1]
[q1]>[/q1]
[q1]>F 2[/q1]
[q1]>[/q1]
[q1]>F 3[/q1]
[q1]>[/q1]
[q1]>F 4[/q1]
[q1]>[/q1]
[q1]>G 1[/q1]
[q1]>[/q1]
[q1]>G 2[/q1]
[q1]>[/q1]
[q1]>G 3[/q1]
[q1]>[/q1]
[q1]>G 4[/q1]
[q1]>[/q1]
[q1]>H 1[/q1]
[q1]>[/q1]
[q1]>H 2[/q1]
[q1]>[/q1]
[q1]>H 3[/q1]
[q1]>[/q1]
[q1]>H 4[/q1]
[q1]>[/q1]
[q1]>[/q1]
[q1]>[/q1]
[q1]>I am trying to find out how many unique combinations there are from this.[/q1]
[q1]>[/q1]
[q1]>It would be nice to know how you work it out too.[/q1]
[q1]>[/q1]
[q1]>I think that due to the restrictions there are only 107 possible combinations, but I could easily[/q1]
[q1]>be well wrong as my math is not that[/q1]
great.
[q1]>[/q1]
[q1]>Also I am interested to know how changing the rules to only having to pick four selections where I[/q1]
[q1]>must pick 1 of each seed but can pick the four from any group as long as I only pick at most 1 from[/q1]
[q1]>each group would effect the possible combinations, I imagine this will increase the possible[/q1]
[q1]>selections by a lot.[/q1]
[q1]>[/q1]
[q1]>Thank you for getting this far[/q1]
[q1]>[/q1]
[q1]>[/q1]