Please help a math dummy

This is racking my brain, please help!

Local bingo hall has a "lotto" using 20 balls numbered 1 thru 20.. Four numbers are selected from the machine.
We choose 4 numbers.
I know the odds of matching all four numbers are 1 in 4845.
And the odds of matching 3 numbers is 1 in 75.7 as there are a total of 64 combinations.

But I have tried repeatedly to write down all 64 combinations, but cannot come up with 64. arggg

Can someone list them for me or show me how to do so in excel?

TIA

Quote: Edpokernut

This is racking my brain, please help!

Local bingo hall has a "lotto" using 20 balls numbered 1 thru 20.. Four numbers are selected from the machine.
We choose 4 numbers.
I know the odds of matching all four numbers are 1 in 4845.
And the odds of matching 3 numbers is 1 in 75.7 as there are a total of 64 combinations.

But I have tried repeatedly to write down all 64 combinations, but cannot come up with 64. arggg

Can someone list them for me or show me how to do so in excel?

TIA

Not an expert. But in any particular group of 4 numbers, there are only 4 ways to match exactly 3 of them.

There are 16 "other" numbers left of 20 possible that you didn't use.

So, if you substitute any of those other numbers for the one NOT selected, you have 17 "other" numbers that have AT LEAST 3 right.

Except.

One of those 16 "other" numbers has to be the 4th number. So you have to subtract that combination group back out.

That leaves you 16 total numbers not drawn.
x 4 ways each combination can have EXACTLY 3 right, 1 wrong. =64.

Which half-answers your question. That's where the 64 comes from (I think), but expressing it as a spreadsheet or series of formulae...well, I've proven many times I don't do that well.

I'll take a crack at the excel.

Example:
- You picked 1,2,3,4

Here are the 4 ways of getting 3 of 4 numbers correct.
1,2,3
1,2,4
1,3,4
2,3,4

16 balls remain for each option...

Here are the 64 ways:


Edit: I don't know why my embedded image isn't working. Babs?

Here is a link.
https://imgur.com/wuH53l3

Mod edit: added .png to your link that didn't have an extension. Got lucky and it worked. BBB

Response to mod edit: thanks BBB. You rock. Love, Prozema.

Quote: Edpokernut

...I have tried repeatedly to write down all 64 combinations...

Let's assume you pick the numbers 1 2 3 and 4. Then ways to get three matches are in two parts (a) Three of the four numbers you've picked (b) One of the numbers you didn't pick.
(a) can be 123 124 134 or 234 (i.e. you can pick which one you didn't match, so there are four ways to di this).
(b) can be any one of 5 thru 20 (i.e. you have sixteen picks).
So the total number of combinations is 4 x 16. 1235 1236 1237 ... 123 20 .. 1245 ... 234 20.

Quote: Edpokernut

And the odds of matching 3 numbers is 1 in 75.7 as there are a total of 64 combinations.

But I have tried repeatedly to write down all 64 combinations, but cannot come up with 64. arggg

Can someone list them for me or show me how to do so in excel?

Here's a "list" if your four numbers are 1, 2, 3, 4:
1, 2, 3, and anything from 5 to 20 - that's 16 combinations
1, 2, 4, and anything from 5 to 20 - that's another 16 combinations
1, 3, 4, and anything from 5 to 20 - that's yet another 16 combinations
2, 3, 4, and anything from 5 to 20 - that's 16 more combinations
Total = 64

Quote: Edpokernut

Can someone list them for me or show me how to do so in excel?TIA

The 64 are easy in Excel.
Try the 720 for 4 choose 2 with your method!

looks like you did 'hammer it out' (using your example of choosing 1,2,3,4)

item	index	item	index
1,2,3,5	1	1,3,4,5	33
1,2,3,6	2	1,3,4,6	34
1,2,3,7	3	1,3,4,7	35
1,2,3,8	4	1,3,4,8	36
1,2,3,9	5	1,3,4,9	37
1,2,3,10	6	1,3,4,10	38
1,2,3,11	7	1,3,4,11	39
1,2,3,12	8	1,3,4,12	40
1,2,3,13	9	1,3,4,13	41
1,2,3,14	10	1,3,4,14	42
1,2,3,15	11	1,3,4,15	43
1,2,3,16	12	1,3,4,16	44
1,2,3,17	13	1,3,4,17	45
1,2,3,18	14	1,3,4,18	46
1,2,3,19	15	1,3,4,19	47
1,2,3,20	16	1,3,4,20	48
1,2,4,5	17	2,3,4,5	49
1,2,4,6	18	2,3,4,6	50
1,2,4,7	19	2,3,4,7	51
1,2,4,8	20	2,3,4,8	52
1,2,4,9	21	2,3,4,9	53
1,2,4,10	22	2,3,4,10	54
1,2,4,11	23	2,3,4,11	55
1,2,4,12	24	2,3,4,12	56
1,2,4,13	25	2,3,4,13	57
1,2,4,14	26	2,3,4,14	58
1,2,4,15	27	2,3,4,15	59
1,2,4,16	28	2,3,4,16	60
1,2,4,17	29	2,3,4,17	61
1,2,4,18	30	2,3,4,18	62
1,2,4,19	31	2,3,4,19	63
1,2,4,20	32	2,3,4,20	64

There are macros that do this real fast, but you have to know how to work with them (and you did not mention that), so here is my Excel using just basic counting functions and the list for each 4C3 is the worksheet,
from that I copied and pasted just the values into 4C3(2) and removed all the columns except the 1st and last. from there it is easy to sort by last column and keep all the 1s.
you have to look to see what I am talking about. It took 1 minute for all the sheets.(I know what I am doing)

I start by listing all the 20Choose4 from here as it is easier for me
https://www.mathsisfun.com/combinatorics/combinations-permutations-calculator.html
imported that into Excel and did the formula for each column. I am very good at copy/paste

IF interested, here is my Excel sheet in Google (I did 4C3 and 4C2)
https://drive.google.com/open?id=1KWudM3qxAfBbl074szcAT-tka7XAIIKU
hope this can help out for the next attempt

Thank you so much everyone! It looks so easy to see it now. Much appreciated!