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a joint combinations problem

Started by MTclip Jan 12, 2007 at 4:34 PM 3 replies 1.1k views

Original Post

Jan 12, 2007 at 4:34 PM

Im am trying to figure out the number of possible cominations of balls for a 24 number bingo game... here is what i have so far.. there are.. B = 3003 combinations I = 3003 combinations N = 1365 combinations G = 3003 combinations O = 3003 combinations how do i find out the possible combinations for all letters combined is it.. n = B*I*N*G*0 r = 5

Zipster

511

Zipster

Jan 12, 2007 at 5:23 PM

Maybe I'm misunderstanding the problem, but if you have 24 positions (5x5 grid minus the free space) and 24 values, the number of possible combinations is (24)₂₄ (the permutation).

MTclip

Author

MTclip

Jan 12, 2007 at 5:30 PM

well order is un important so i chose combination...

I am trying to figure out the number of different ball combinations..

B has balls# 1 - 15 and 5 are in a combination
I 16 - 30 & 5 in combo
N 31 - 45 & 4 in combo
G 46 - 60 & 5 in combo
0 60 - 75 & 5 in combo

Zipster

511

Zipster

Jan 12, 2007 at 6:16 PM

Ah I forgot that you can only have certain number ranges in each column. In that case the values you have for each column are correct, and all you need to do is multiply them together to get the total number of combinations for the whole board.

glSmurf

Jan 13, 2007 at 3:26 AM

The number of ways to select (in no specific order) k elements from a set of n is n!/[k!(n-k)!]
So, for each of the letters there is a set of 15, and you wanna select 5 out of those.

B  1-15 = 15 => 15!/[5!(15-5)!] = 3003I 16-30 = 15 => 15!/[5!(15-5)!] = 3003N 31-45 = 15 => 15!/[5!(15-5)!] = 3003G 46-60 = 15 => 15!/[5!(15-5)!] = 30030 61-75 = 15 => 15!/[5!(15-5)!] = 3003

To combine all 5 letters we simply multilpy them (3003⁵ = 244217432431215243).

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