How many combinations??

[Eclectic Lady]

Hello,

This may very well not be the place to post this question but I'm a writer not a math wiz and quite simply don't know how to figure this out.

I'm writing a newspaper article on hoarding and would like to determine how many different Christmas trees I can decorate using seven variables (different balls, bobbles and other embellishments) with a maximum grouping of two variables per tree/year.

For the sake of the calculation let's pretend there are equal amounts of each of the following items: Red satin balls; gold satin balls; red glitter icicles; gold glitter icicles; red mirrored snowflakes; gold mirrored snowflakes and red silk poinsettia bracts.

To avoid clutter—difficult for most hoarders I know—I'm limiting the combinations used each year to two. Sooo, one year I use red glitter icicles with gold mirrored snowflakes. . .the next year I use gold satin balls and red poinsettia bracts.

How many years can I decorate the same artificial tree without repeating the combinations? Is it even within the span​ of human life expectancy?

Thanks!!
Sheree

 

[sheetspread]

try shg's chinese food menu:

https://app.box.com/shared/ubd28tissi

and divide the number of combinations by 2 or however many per year.

 

[shg]

=combin(7, 2) returns 21.

 

[Eclectic Lady]

Abac ad ae af ag
bc bd be bf bg
cd ce cf cg
de df dg
ef eg
fg

 

[Eclectic Lady]

Thanks Sheetspread and Shg...

I looked at the Chinese Food Menu and was VERY intrigued but don't have the time now to sort it out (but will return someday). . .

Shg: Your formula "=combin(7,2) returns 21" was also interesting but I'm a bit rusty on which numbers/factors to plug in where. . .

BUT I did my own little diagram to see if I could come up with 21 and voila! It worked:

ab ac ad ae af ag
bc bd be bf bg
cd ce cf cg
de df dg
ef eg
fg

21!!

Is that the answer then? Seven different decorations....when used two at a time. . .will yield 21 different combinations?

Wow....if that's the answer then there's hope. . .I might live long enough to use all 21 combinations....

THANKS
Sheree

 

[Eclectic Lady]

The alignment of my diagram above went wacky when I hit Post, thus explaining why it doesn't make sense now. In reality my columns were aligned properly...

 

[shg]

try shg's chinese food menu:

https://app.box.com/shared/ubd28tissi

There's a later version at https://app.box.com/s/47b28f19d794b25511be

 

[sheetspread]

Is that the answer then? Seven different decorations....when used two at a time. . .will yield 21 different combinations?

There's a later version at https://app.box.com/s/47b28f19d794b25511be

Using the menu program (yes I should have found the later version, thanks for posting it, I was wondering why the older one didn't have the macro I remembered):

Excel 2010
	B	C	D	E	F	G	H	I	J	K
2	Cum:	49	7							1,1
3	Cnt:	7	7							1,2
4	Header:	1	2							1,3
5	Inputs:	1	1							1,4
6		2	2							1,5
7		3	3							1,6
8		4	4							1,7
9		5	5							2,2
10		6	6							2,3
11		7	7							2,4
12										2,5
13										2,6
14	#									2,7
15	1	1	1		1,1					3,3
16	2	1	2		1,2					3,4
17	3	1	3		1,3					3,5
18	4	1	4		1,4					3,6
19	5	1	5		1,5					3,7
20	6	1	6		1,6					4,4
21	7	1	7		1,7					4,5
22	8	2	1		1,2					4,6
23	9	2	2		2,2					4,7
24	10	2	3		2,3					5,5
25	11	2	4		2,4					5,6
26	12	2	5		2,5					5,7
27	13	2	6		2,6					6,6
28	14	2	7		2,7					6,7
29	15	3	1		1,3					7,7
30	16	3	2		2,3
31	17	3	3		3,3
32	18	3	4		3,4
33	19	3	5		3,5
34	20	3	6		3,6
35	21	3	7		3,7
36	22	4	1		1,4
37	23	4	2		2,4
38	24	4	3		3,4
39	25	4	4		4,4
40	26	4	5		4,5
41	27	4	6		4,6
42	28	4	7		4,7
43	29	5	1		1,5
44	30	5	2		2,5
45	31	5	3		3,5
46	32	5	4		4,5
47	33	5	5		5,5
48	34	5	6		5,6
49	35	5	7		5,7
50	36	6	1		1,6
51	37	6	2		2,6
52	38	6	3		3,6
53	39	6	4		4,6
54	40	6	5		5,6
55	41	6	6		6,6
56	42	6	7		6,7
57	43	7	1		1,7
58	44	7	2		2,7
59	45	7	3		3,7
60	46	7	4		4,7
61	47	7	5		5,7
62	48	7	6		6,7
63	49	7	7		7,7
using Formulas

Cell Formulas
Range	Formula
C2	=PRODUCT(relS:$D$3)
C3	=COUNTA(Symbols)
C15	=INDEX(Symbols, MOD(INT((Line - 1) * Cnt / Cum), Cnt) + 1)
B15	=ROW()-ROW(B$14)
D15	=INDEX(Symbols, MOD(INT((Line - 1) * Cnt / Cum), Cnt) + 1)
F15	=MIN(C15:D15)&","&MAX(C15:D15)

Named Ranges
Name	Refers To	Cells
'using Formulas'!Cnt	='using Formulas'!B$3
'using Formulas'!Cum	='using Formulas'!B$2
'using Formulas'!Line	='using Formulas'!$B2
'using Formulas'!relS	='using Formulas'!B3
'using Formulas'!Symbols	=INDEX('using Formulas'!B$4:B$14, 2):INDEX('using Formulas'!B$4:B$14, ROWS('using Formulas'!B$4:B$14) - 1)

(Paste to column K, remove duplicates and identical pairs)

 

[Micron]

This all looks like a lot of work when you could just use the COMBIN function in Excel, right? It gives the answer 21.

 

[sheetspread]

Yes but if you need the combinations instead of just the count.........