Math Is Fun Forum

Okay, I found the time to recalculate the number of combinations with the following parameters

Max on Roster = 12
Made up of a combination of QBs, RBs, WRs, & TEs
Each position has a minimum and maximum allowed as shown below

  QBs (Min = 1, Max = 7)
  RBs (Min = 2, Max = 8
  WRs (Min = 2, Max =8)
  TEs (Min = 1, Max = 7

This time I came up with 80 combinations (no repeat, order doesn't matter) as shown in the below list.

Did I get it correct this time?

#    QB   RB  WR TE  TOT
01    1    8    2    1    12
02    1    7    3    1    12
03    1    7    2    2    12
04    1    6    3    2    12
05    1    6    2    3    12
06    1    5    4    2    12
07    1    5    3    3    12
08    1    5    2    4    12
09    1    4    5    2    12
10    1    4    4    3    12
11    1    4    3    4    12
12    1    4    2    5    12
13    1    3    7    1    12
14    1    3    6    2    12
15    1    3    5    3    12
16    1    3    4    4    12
17    1    3    3    5    12
18    1    3    2    6    12
19    1    2    8    1    12
20    1    2    7    2    12
21    1    2    6    3    12
22    1    2    5    4    12
23    1    2    4    5    12
24    1    2    3    6    12
25    1    2    2    7    12
26    2    7    2    1    12
27    2    6    3    1    12
28    2    6    2    2    12
29    2    5    4    1    12
30    2    5    3    2    12
31    2    5    2    3    12
32    2    4    5    1    12
33    2    4    4    2    12
34    2    4    3    3    12
35    2    4    2    4    12
36    2    3    6    1    12
37    2    3    5    2    12
38    2    3    4    3    12
39    2    3    3    4    12
40    2    3    2    5    12
41    2    2    7    1    12
42    2    2    6    2    12
43    2    2    5    3    12
44    2    2    4    4    12
45    2    2    3    5    12
46    2    2    2    6    12
47    3    6    2    1    12
48    3    5    3    1    12
49    3    5    2    2    12
50    3    4    3    2    12
51    3    4    2    3    12
52    3    3    5    1    12
53    3    3    4    2    12
54    3    3    3    3    12
55    3    3    2    4    12
56    3    2    6    1    12
57    3    2    5    2    12
58    3    2    4    3    12
59    3    2    3    4    12
60    3    2    2    5    12
61    4    5    2    1    12
62    4    4    3    1    12
63    4    4    2    2    12
64    4    3    4    1    12
65    4    3    3    2    12
66    4    3    2    3    12
67    4    2    5    1    12
68    4    2    4    2    12
69    4    2    3    3    12
70    4    2    2    4    12
71    5    4    2    1    12
72    5    3    3    1    12
73    5    3    2    2    12
74    5    2    4    1    12
75    5    2    3    2    12
76    5    2    2    3    12
77    6    3    2    1    12
78    6    2    3    1    12
79    6    2    2    2    12
80    7    2    2    1    12

I'm baaaack!

First, you are correct phrontister.  Sorry it took so long to reply.  And I've corrected the post.

But I have another combination of football positions that I would appreciate it if someone would verify my final number of combinations that can make up a fantasy football roster

The parameters are:

Max on Roster = 12
Made up of a combination of QBs, RBs, WRs, & TEs CORRECTED
Each position has a minimum and maximum allowed as shown below

  QBs (Min = 1, Max = 7)
  RBs (Min = 2, Max = 8
  WRs (Min = 2, Max =8)
  TEs (Min = 1, Max = 7) CORRECTED

I came up with 34 combinations (no repeat, order doesn't matter) as shown in the below list.

Am I correct in my count of 34 different combinations?

QB RB WR TE  TOT
7    2    2    1    12
6    3    2    1    12
6    2    3    1    12
6    2    2    2    12
5    4    2    1    12
5    2    4    1    12
5    2    2    3    12
4    5    2    1    12
4    2    5    1    12
4    2    2    4    12
3    6    2    1    12
3    2    6    1    12
3    2    2    5    12
2    7    2    1    12
2    2    7    1    12
2    2    2    6    12
1    8    2    1    12
1    7    3    1    12
1    7    2    2    12
1    6    4    1    12
1    6    2    3    12
1    5    5    1    12
1    5    2    4    12
1    4    6    1    12
1    4    2    5    12
1    3    7    1    12
1    3    2    6    12
1    2    8    1    12
1    2    7    2    12
1    2    6    3    12
1    2    5    4    12
1    2    4    5    12
1    2    3    6    12
1    2    2    7    12

Total = 34

Thanks - Mitch

As I said, I'm really a dunce with math - especially algebra, so I'm not completely understanding what you are calculating.

Are you calculating all the combinations that DON'T EXCEED 40?

Maybe a couple of examples would clear the fog for me ????

Thanks

Sorry for the confusion

Each Combination does not have repetition and order doesn't matter, i.e.

2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 3, 1 is the same as

3, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2 or

2, 2, 2, 2, 2, 2, 1, 3, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, etc.

Waiting with baited breath

BTW - I'm a math midget, so be gentle

Bob - Received the SS; reviewing it and will get back to you (et al).

Sorry for my absence - been working on another project.

How do I get to your spreadsheet (never used Google Drive) so I can compare your results with mine?

-- Mitch

Sounds like a plan.

-- Mitch

Maybe this will help -

In the 'Configuration Spreadsheet" you''ll see a list (I2 thru I9) of 8 Entries [sic combinations) of a Roster that can comprise the lineup.

The 1st Combination (QB1, TE1, PK1) is utilized Group 1; the 2nd Combination (QB1, TE, PK2) is shown in Group 2 and so forth.

One takes the original configuration , multiply by 8 (# of possible combinations of QB1, QB2,TE1, TE2, PK1, PK2 which is 7) to come up with a possible 56 different configuration for the Roster settings.

Make more sense?

The most obvious reason to me is that you have 2 QBs & 2 PKs in the starting lineup. (lines 1 thru 4 & lines 4, 7, 10 & 11 respectively)

Remember, only 1 QB, 1 PK & 1 TM can be in the starting lineup.

Additionally, don't forget that we are looking for all the 10-men combinations that can be had using the 14-man Roster configuration of:

2 QBs (QB1 & QB2)
3 RBs, (RB1, RB2 & RB3)
4 WRs, (WR1, WR2, WR3 & WR4)
2 TEs (TE1 & TE2)
2 PKs (PK1 & PK2)
1 TM (TM1)

-- Mitch

phrontister,  Good catch.

Because of the Lineup limitations, you are correct, only five configurations are possible for the lineup submission.  I've corrected those posts erroneously showing six.

I rechecked my calculations (spreadsheets) and also what Bob posted here and in all cases it looks as though the calculations only allowed 2 TEs.  So it seems everything is good in that regard.

Again, thanks for the heads-up.

++++++++++

Bob, it looks to me that the 86 combinations you came up with in post #19 is the number of different player combinations for the five lineup configurations.  Here's the MIF calculation:

Combinations without repetition (n=10, r=7)
Using Items: rb1,rb2,rb3,rb4,wr1,wr2,wr3,wr4,te1,te2
Using Rule: has 2 of: rb1,rb2,rb3,rb4
Using Rule: has 2 of: wr1,wr2,wr3,wr1
Using Rule: has 1 of: te1,te2

List has 86 entries.  [ Add 1 QB, 1 PK & 1 TM to each combination to come up with the 10-man lineup ]
rb1,rb2,rb3,rb4,wr1,wr2,te1
rb1,rb2,rb3,rb4,wr1,wr2,te2
rb1,rb2,rb3,rb4,wr1,wr3,te1
rb1,rb2,rb3,rb4,wr1,wr3,te2
rb1,rb2,rb3,rb4,wr2,wr3,te1
rb1,rb2,rb3,rb4,wr2,wr3,te2
rb1,rb2,rb3,wr1,wr2,wr3,te1
rb1,rb2,rb3,wr1,wr2,wr3,te2
rb1,rb2,rb3,wr1,wr2,wr4,te1
rb1,rb2,rb3,wr1,wr2,wr4,te2
rb1,rb2,rb3,wr1,wr2,te1,te2
rb1,rb2,rb3,wr1,wr3,wr4,te1
rb1,rb2,rb3,wr1,wr3,wr4,te2
rb1,rb2,rb3,wr1,wr3,te1,te2
rb1,rb2,rb3,wr2,wr3,wr4,te1
rb1,rb2,rb3,wr2,wr3,wr4,te2
rb1,rb2,rb3,wr2,wr3,te1,te2
rb1,rb2,rb4,wr1,wr2,wr3,te1
rb1,rb2,rb4,wr1,wr2,wr3,te2
rb1,rb2,rb4,wr1,wr2,wr4,te1
rb1,rb2,rb4,wr1,wr2,wr4,te2
rb1,rb2,rb4,wr1,wr2,te1,te2
rb1,rb2,rb4,wr1,wr3,wr4,te1
rb1,rb2,rb4,wr1,wr3,wr4,te2
rb1,rb2,rb4,wr1,wr3,te1,te2
rb1,rb2,rb4,wr2,wr3,wr4,te1
rb1,rb2,rb4,wr2,wr3,wr4,te2
rb1,rb2,rb4,wr2,wr3,te1,te2
rb1,rb2,wr1,wr2,wr3,wr4,te1
rb1,rb2,wr1,wr2,wr3,wr4,te2
rb1,rb2,wr1,wr2,wr3,te1,te2
rb1,rb2,wr1,wr2,wr4,te1,te2
rb1,rb2,wr1,wr3,wr4,te1,te2
rb1,rb2,wr2,wr3,wr4,te1,te2
rb1,rb3,rb4,wr1,wr2,wr3,te1
rb1,rb3,rb4,wr1,wr2,wr3,te2
rb1,rb3,rb4,wr1,wr2,wr4,te1
rb1,rb3,rb4,wr1,wr2,wr4,te2
rb1,rb3,rb4,wr1,wr2,te1,te2
rb1,rb3,rb4,wr1,wr3,wr4,te1
rb1,rb3,rb4,wr1,wr3,wr4,te2
rb1,rb3,rb4,wr1,wr3,te1,te2
rb1,rb3,rb4,wr2,wr3,wr4,te1
rb1,rb3,rb4,wr2,wr3,wr4,te2
rb1,rb3,rb4,wr2,wr3,te1,te2
rb1,rb3,wr1,wr2,wr3,wr4,te1
rb1,rb3,wr1,wr2,wr3,wr4,te2
rb1,rb3,wr1,wr2,wr3,te1,te2
rb1,rb3,wr1,wr2,wr4,te1,te2
rb1,rb3,wr1,wr3,wr4,te1,te2
rb1,rb3,wr2,wr3,wr4,te1,te2
rb1,rb4,wr1,wr2,wr3,wr4,te1
rb1,rb4,wr1,wr2,wr3,wr4,te2
rb1,rb4,wr1,wr2,wr3,te1,te2
rb1,rb4,wr1,wr2,wr4,te1,te2
rb1,rb4,wr1,wr3,wr4,te1,te2
rb1,rb4,wr2,wr3,wr4,te1,te2
rb2,rb3,rb4,wr1,wr2,wr3,te1
rb2,rb3,rb4,wr1,wr2,wr3,te2
rb2,rb3,rb4,wr1,wr2,wr4,te1
rb2,rb3,rb4,wr1,wr2,wr4,te2
rb2,rb3,rb4,wr1,wr2,te1,te2
rb2,rb3,rb4,wr1,wr3,wr4,te1
rb2,rb3,rb4,wr1,wr3,wr4,te2
rb2,rb3,rb4,wr1,wr3,te1,te2
rb2,rb3,rb4,wr2,wr3,wr4,te1
rb2,rb3,rb4,wr2,wr3,wr4,te2
rb2,rb3,rb4,wr2,wr3,te1,te2
rb2,rb3,wr1,wr2,wr3,wr4,te1
rb2,rb3,wr1,wr2,wr3,wr4,te2
rb2,rb3,wr1,wr2,wr3,te1,te2
rb2,rb3,wr1,wr2,wr4,te1,te2
rb2,rb3,wr1,wr3,wr4,te1,te2
rb2,rb3,wr2,wr3,wr4,te1,te2
rb2,rb4,wr1,wr2,wr3,wr4,te1
rb2,rb4,wr1,wr2,wr3,wr4,te2
rb2,rb4,wr1,wr2,wr3,te1,te2
rb2,rb4,wr1,wr2,wr4,te1,te2
rb2,rb4,wr1,wr3,wr4,te1,te2
rb2,rb4,wr2,wr3,wr4,te1,te2
rb3,rb4,wr1,wr2,wr3,wr4,te1
rb3,rb4,wr1,wr2,wr3,wr4,te2
rb3,rb4,wr1,wr2,wr3,te1,te2
rb3,rb4,wr1,wr2,wr4,te1,te2
rb3,rb4,wr1,wr3,wr4,te1,te2
rb3,rb4,wr2,wr3,wr4,te1,te2

Also, since #2 & #6, as phrontister pointed out, are the same does that mean there are only 45 combinations or is there a typo?  FOLLOW-UP.  I checked and I'm pretty sure it's a typo.

++++++++++

Food for thought:  Would it help if I tried to consolidate all these 26 posts into one cohesive post to make sure we are all on the same page?  Or are we good?

-- Mitch