# Need help with math problem - possible combinations **URL:** \ **Category:** Factual Questions\ **Created:** [December 2, 2014, 6:17pm UTC](https://boards.straightdope.com/t/need-help-with-math-problem-possible-combinations/706148 "2014-12-02T18:17:30Z")\ **Posts on this page:** 13\ **Page:** 1
**Author:** ![StreetHockeyGuy](https://avatars.discourse-cdn.com/v4/letter/s/dfb087/32.png) [@StreetHockeyGuy](https://boards.straightdope.com/u/StreetHockeyGuy)\ **Post date:** [December 2, 2014, 6:17pm UTC](https://boards.straightdope.com/t/need-help-with-math-problem-possible-combinations/706148/1 "2014-12-02T18:17:30Z")
I am building a widget with 10 components. Each component can have 1 of 30 colors. 1 of the 10 components has 5 different types. Another one of the 10 components has 15 different types. Can someone please help me figure out how many possible combinations there are? Needless to say I’ve googled this and have come up empty with this n! over r! crap… Thanks in advance! ---
**Author:** ![Snarky\_Kong](https://avatars.discourse-cdn.com/v4/letter/s/a183cd/32.png) [@Snarky\_Kong](https://boards.straightdope.com/u/Snarky_Kong)\ **Post date:** [December 2, 2014, 6:38pm UTC](https://boards.straightdope.com/t/need-help-with-math-problem-possible-combinations/706148/2 "2014-12-02T18:38:24Z")
Do the other 8 components only have 1 type? If so (30^8)(150)(450)~=4\*10^16 ---
**Author:** ![DataX](https://avatars.discourse-cdn.com/v4/letter/d/e99b99/32.png) [@DataX](https://boards.straightdope.com/u/DataX)\ **Post date:** [December 2, 2014, 6:41pm UTC](https://boards.straightdope.com/t/need-help-with-math-problem-possible-combinations/706148/3 "2014-12-02T18:41:04Z")
If 8 of the widgets have only one type than do it this way: 8 \* 30 \* 1 (only to make it easy to understand) = 240 1 \* 30 \* 5 = 150 1 \* 30 \* 15 = 450 240 + 150 + 450 = 840 ---
**Author:** ![MrFloppy](https://avatars.discourse-cdn.com/v4/letter/m/43a26b/32.png) [@MrFloppy](https://boards.straightdope.com/u/MrFloppy)\ **Post date:** [December 2, 2014, 6:42pm UTC](https://boards.straightdope.com/t/need-help-with-math-problem-possible-combinations/706148/4 "2014-12-02T18:42:02Z")
Seems simple enough. The number of combinations of the 10 widgets would be (30^10). Then multiply that by 75 (5\*15) for the multiple types of widget in two of the locations. So 75(30^10) or about 44 286 750 000 000 000. ---
**Author:** ![DataX](https://avatars.discourse-cdn.com/v4/letter/d/e99b99/32.png) [@DataX](https://boards.straightdope.com/u/DataX)\ **Post date:** [December 2, 2014, 6:42pm UTC](https://boards.straightdope.com/t/need-help-with-math-problem-possible-combinations/706148/5 "2014-12-02T18:42:19Z")
> [@Snarky\_Kong](#): > > Do the other 8 components only have 1 type? If so (30^8)(150)(450)~=4\*10^16 Are you sure you multiply them? ---
**Author:** ![MrFloppy](https://avatars.discourse-cdn.com/v4/letter/m/43a26b/32.png) [@MrFloppy](https://boards.straightdope.com/u/MrFloppy)\ **Post date:** [December 2, 2014, 6:51pm UTC](https://boards.straightdope.com/t/need-help-with-math-problem-possible-combinations/706148/6 "2014-12-02T18:51:49Z")
OP. are the two widgets with multiple types always in the same location or can they be in any location? My answer was for them being in a particular location for example the 4th and 8th location. ---
**Author:** ![The\_Hamster\_King](https://avatars.discourse-cdn.com/v4/letter/t/8edcca/32.png) [@The\_Hamster\_King](https://boards.straightdope.com/u/The_Hamster_King)\ **Post date:** [December 2, 2014, 6:51pm UTC](https://boards.straightdope.com/t/need-help-with-math-problem-possible-combinations/706148/7 "2014-12-02T18:51:50Z")
Can the colors repeat or does each component have a unique color? If the colors are unique then the answer is: 30 \* 29 \* 28 \* 27 \* 26 \* 25 \* 24 \* 23 \* 22 \* 21 \* 5 \* 15 or approximately 8.2 quadrillion. ---
**Author:** ![Snarky\_Kong](https://avatars.discourse-cdn.com/v4/letter/s/a183cd/32.png) [@Snarky\_Kong](https://boards.straightdope.com/u/Snarky_Kong)\ **Post date:** [December 2, 2014, 6:52pm UTC](https://boards.straightdope.com/t/need-help-with-math-problem-possible-combinations/706148/8 "2014-12-02T18:52:07Z")
> [@DataX](#): > > Are you sure you multiply them? Yes. Imagine you have 2 things that can be A, B, or C. The possible combinations are: AA AB AC BA BB BC CA CB CC 9 things, not 6 as adding them would give you. ---
**Author:** ![StreetHockeyGuy](https://avatars.discourse-cdn.com/v4/letter/s/dfb087/32.png) [@StreetHockeyGuy](https://boards.straightdope.com/u/StreetHockeyGuy)\ **Post date:** [December 2, 2014, 6:54pm UTC](https://boards.straightdope.com/t/need-help-with-math-problem-possible-combinations/706148/9 "2014-12-02T18:54:18Z")
Maybe I didn’t explain the problem well enough. Let me use a tangible example. I’m creating a build your own guitar with prefabricated parts that effective snap or screw together, so that the average idiot can assemble it. Let’s not argue about whether or not it works. IT’s for an imaginary business plan for school. So I have come up with a guitar that has 10 component pieces. Of the ten components, 8 of them are only 1 type. The fretboard has 5 different variations. The strings come in 15 different sets. Each component, the 8 individual ones plus the fretboard and the strings can each come in 1 of 30 possible colors. I am trying to figure out how many possible combinations there are with these choices. Thanks! ---
**Author:** ![StreetHockeyGuy](https://avatars.discourse-cdn.com/v4/letter/s/dfb087/32.png) [@StreetHockeyGuy](https://boards.straightdope.com/u/StreetHockeyGuy)\ **Post date:** [December 2, 2014, 6:59pm UTC](https://boards.straightdope.com/t/need-help-with-math-problem-possible-combinations/706148/10 "2014-12-02T18:59:55Z")
> [@The\_Hamster\_King](#): > > Can the colors repeat or does each component have a unique color? > > If the colors are unique then the answer is: > > 30 \* 29 \* 28 \* 27 \* 26 \* 25 \* 24 \* 23 \* 22 \* 21 \* 5 \* 15 > > or approximately 8.2 quadrillion. The colors can repeat. So if red is one of the colors, then the entire guitar can be red. ---
**Author:** ![MrFloppy](https://avatars.discourse-cdn.com/v4/letter/m/43a26b/32.png) [@MrFloppy](https://boards.straightdope.com/u/MrFloppy)\ **Post date:** [December 2, 2014, 7:02pm UTC](https://boards.straightdope.com/t/need-help-with-math-problem-possible-combinations/706148/11 "2014-12-02T19:02:00Z")
Then my answer stands. Imagine you have only one set of strings and one fret board, the combinations would be 30x30x30x30x30x30x30x30x30x30 or 30^10. There are 5 fretboards so multiply that by 5 and there are 15 sets of strings so multimply that by 15. The answer is 75(30^10) or 44 286 750 000 000 000 ---
**Author:** ![StreetHockeyGuy](https://avatars.discourse-cdn.com/v4/letter/s/dfb087/32.png) [@StreetHockeyGuy](https://boards.straightdope.com/u/StreetHockeyGuy)\ **Post date:** [December 2, 2014, 7:41pm UTC](https://boards.straightdope.com/t/need-help-with-math-problem-possible-combinations/706148/12 "2014-12-02T19:41:06Z")
Awesome, thanks so much for helping. ---
**Author:** ![Tim\_T-Bonham.net](https://avatars.discourse-cdn.com/v4/letter/t/46a35a/32.png) [@Tim\_T-Bonham.net](https://boards.straightdope.com/u/Tim_T-Bonham.net)\ **Post date:** [December 2, 2014, 10:08pm UTC](https://boards.straightdope.com/t/need-help-with-math-problem-possible-combinations/706148/13 "2014-12-02T22:08:03Z")
ny real man would tell you there just\*\* aren’t\*\* 30 different colors!