haha just watching this after a trip to mexico. i need to do a bike food tour like this next time. also, math person here, phil, you were right initially this is a "combination" not a "permutation" ;) permutation is only when you care about the order the ingredients go into the taco(in which there are wayyy more possibilities and involves factorials). since this is just a combination, for each sauce there are only 2 possibilities: in or out. so only 2*2*2*2*2*2*2*2 = 2^8 = 256
Someone better at math can check my calc. If there are 8 salsas and you can choose 0 to 8 in any combination, there are 256 different ways to do it (1 way to choose 0 + 8 ways to choose 1 + 28 ways to choose 2 + ... etc).
The number of possible combinations with up to 8 ingredients (since you don't have to take all 8 at the same time), duplicates removed, should be: 1 Ingredient: 8/1! = 8 (you can pick either one) 2 Ingredients: (8x7)/2! = 28 (chose any one and then any one of the remaining 7, etc.) 3 Ingredients: (8x7x6)/3! = 56 4 Ingredients: (8x7x6x5)/4! = 70 5 Ingredients: (8x7x6x5x4)/5! = 56 6 Ingredients: (8x7x6x5x4x3)/6! = 28 7 Ingredients: (8x7x6x5x4x3x2)/7! = 8 (leave one out) 8 Ingredients: 8!/8! = 1 (only one possibility to chose all 8) = 255 unique combinations of 1..8 different ingredients. Ignored the case with 0 ingredients. If you interpret the 8 ingredients as 8 bits that can be set or not, it is obvious why there are 2^8=256 combinations..
@@marcj8464 That would have been a bit much. All permutations would be 8!, but if you always mix together all eight fillings, you will always end up with a taco including all eight ingredients - so you have 40.320 ways to make the same exact same taco :)
Pepe is the best! Nice video Phil 🙌
Properly epic ride!
Everything looked so bright and fresh 🤩🤩🤩
haha just watching this after a trip to mexico. i need to do a bike food tour like this next time. also, math person here, phil, you were right initially this is a "combination" not a "permutation" ;) permutation is only when you care about the order the ingredients go into the taco(in which there are wayyy more possibilities and involves factorials). since this is just a combination, for each sauce there are only 2 possibilities: in or out. so only 2*2*2*2*2*2*2*2 = 2^8 = 256
I just finished eating and now I'm hungry again. Thanks Phil.
Mentioning "wine tour" seemed to get her attention 😀
Looks great!
Will this ride be on Strava? 😂
It is!
surely there's a cycling/speed eating KOM for this route...
Good luck eating Chicken in Mexico. I ate near pyramids, high tourist attraction, still I got a bug had no appetite for 3 months and lost 10kg
Someone better at math can check my calc. If there are 8 salsas and you can choose 0 to 8 in any combination, there are 256 different ways to do it (1 way to choose 0 + 8 ways to choose 1 + 28 ways to choose 2 + ... etc).
It’s either 8 factorial or 8^8. That’s as far as my memory gets us
The number of possible combinations with up to 8 ingredients (since you don't have to take all 8 at the same time), duplicates removed, should be:
1 Ingredient: 8/1! = 8 (you can pick either one)
2 Ingredients: (8x7)/2! = 28 (chose any one and then any one of the remaining 7, etc.)
3 Ingredients: (8x7x6)/3! = 56
4 Ingredients: (8x7x6x5)/4! = 70
5 Ingredients: (8x7x6x5x4)/5! = 56
6 Ingredients: (8x7x6x5x4x3)/6! = 28
7 Ingredients: (8x7x6x5x4x3x2)/7! = 8 (leave one out)
8 Ingredients: 8!/8! = 1 (only one possibility to chose all 8)
= 255 unique combinations of 1..8 different ingredients. Ignored the case with 0 ingredients.
If you interpret the 8 ingredients as 8 bits that can be set or not, it is obvious why there are 2^8=256 combinations..
Thanks, that was going to bug me. I knew 8^8 wasn't quite right.
@@marcj8464 That would have been a bit much. All permutations would be 8!, but if you always mix together all eight fillings, you will always end up with a taco including all eight ingredients - so you have 40.320 ways to make the same exact same taco :)