Flavors
You are an entrepreneur trying to come up with a new flavor to excite the taste buds of the worlds population, and in the process reap the monetary rewards. You have chosen 6 beginning flavors from which to formulate your new flavor:
astringent, bitter, sour, pungent, saline, and sweet (each of these is a new unique flavor you developed)
Given that one test means either:
* selecting one of the 6 unique flavors as the new flavor
or
* combining an equal amount of 2 or more flavors to produce a unique flavor
How many tests are necessary to try all the possibilities?
astringent, bitter, sour, pungent, saline, and sweet (each of these is a new unique flavor you developed)
Given that one test means either:
* selecting one of the 6 unique flavors as the new flavor
or
* combining an equal amount of 2 or more flavors to produce a unique flavor
How many tests are necessary to try all the possibilities?
posted by Zaux at
7:30 AM
6 Comments:
63 varieties.
All based on permutations:
nPr = n!/((n-r)!*r!)), where n = 6 and r = 1 to 6.
1 flavour => 6 ways
2 flavours = 15 ways
3 flavours => 20 ways
4 flavours => 15 ways
5 flavours => 6 ways
6 flavours => 1 way
Another way (quicker) is to notice that either you do or don't include a flavour. So for each flavour there are two choices, include or not included. That give 2^6 combinations. Obviously one combination corresponds to no tastes at all. So 2^6 - 1 = 63 unique flavours.
If there were n original flavours, you could come up with 2^n - 1 combined flavours.
I'll stop there.
Flavors
Must add possibilities of selecting:
1 flavor
2 flavors
3 flavors
4 flavors
5 flavors
6 flavors
Calculate using combination formula
C(B,C)=B!/((B-C)!*C!)
6C1=6
6C2=15
6C3=20
6C4=15
6C5=6
6C6=1
6+15+20+15+6+1= 63
Answer:
63
Cam
Chris,
Looks like we followed the same method. Not to split hairs but, the formula you used is for combinations not permutations i.e. the order doesn't matter. I suspect you know that, but you just happened to use the wrong word on this occasion.
Cam
Hi Cam, I'm always doing that.
.. but at least you fell into the same trap as I originally did, and didn't directly say 2^6 - 1 = 63 for the total number of combinations ;)
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