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Posted by markr on 19/6/2009, 9:18 pm, in reply to "Re: Singing Competition"
I don't think I've got it wrong, but here's my data for you to check. Pick a row you disagree with and we can discuss it further. In each row:
- the first number is the number of ways to permute the partition
- the second number is the number of ways to permute the people in a partition
- the third number is the product of the first two
- the numbers separated by commas are the partitions.
The answer is the sum of the numbers in the third column.
1 1 1 11
2 11 22 10,1
2 55 110 9,2
3 110 330 9,1,1
2 165 330 8,3
6 495 2970 8,2,1
4 990 3960 8,1,1,1
2 330 660 7,4
6 1320 7920 7,3,1
3 1980 5940 7,2,2
12 3960 47520 7,2,1,1
5 7920 39600 7,1,1,1,1
2 462 924 6,5
6 2310 13860 6,4,1
6 4620 27720 6,3,2
12 9240 110880 6,3,1,1
12 13860 166320 6,2,2,1
20 27720 554400 6,2,1,1,1
6 55440 332640 6,1,1,1,1,1
3 2772 8316 5,5,1
6 6930 41580 5,4,2
12 13860 166320 5,4,1,1
3 9240 27720 5,3,3
24 27720 665280 5,3,2,1
20 55440 1108800 5,3,1,1,1
4 41580 166320 5,2,2,2
30 83160 2494800 5,2,2,1,1
30 166320 4989600 5,2,1,1,1,1
7 332640 2328480 5,1,1,1,1,1,1
3 11550 34650 4,4,3
12 34650 415800 4,4,2,1
10 69300 693000 4,4,1,1,1
12 46200 554400 4,3,3,1
12 69300 831600 4,3,2,2
60 138600 8316000 4,3,2,1,1
30 277200 8316000 4,3,1,1,1,1
20 207900 4158000 4,2,2,2,1
60 415800 24948000 4,2,2,1,1,1
42 831600 34927200 4,2,1,1,1,1,1
8 1663200 13305600 4,1,1,1,1,1,1,1
4 92400 369600 3,3,3,2
10 184800 1848000 3,3,3,1,1
30 277200 8316000 3,3,2,2,1
60 554400 33264000 3,3,2,1,1,1
21 1108800 23284800 3,3,1,1,1,1,1
5 415800 2079000 3,2,2,2,2
60 831600 49896000 3,2,2,2,1,1
105 1663200 174636000 3,2,2,1,1,1,1
56 3326400 186278400 3,2,1,1,1,1,1,1
9 6652800 59875200 3,1,1,1,1,1,1,1,1
6 1247400 7484400 2,2,2,2,2,1
35 2494800 87318000 2,2,2,2,1,1,1
56 4989600 279417600 2,2,2,1,1,1,1,1
36 9979200 359251200 2,2,1,1,1,1,1,1,1
10 19958400 199584000 2,1,1,1,1,1,1,1,1,1
1 39916800 39916800 1,1,1,1,1,1,1,1,1,1,1
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