To determine the total number of ancestors a person has going back 10 generations, we can use the formula for ancestors in each generation. Each person has two parents, which doubles for each preceding generation.
The number of ancestors in each generation can be calculated as follows:
- Generation 0 (the person): 1
- Generation 1 (parents): 2^1 = 2
- Generation 2 (grandparents): 2^2 = 4
- Generation 3 (great-grandparents): 2^3 = 8
- Generation 4: 2^4 = 16
- Generation 5: 2^5 = 32
- Generation 6: 2^6 = 64
- Generation 7: 2^7 = 128
- Generation 8: 2^8 = 256
- Generation 9: 2^9 = 512
- Generation 10: 2^10 = 1024
Now we can sum the ancestors back to the 10th generation:
1 (yourself) + 2 (parents) + 4 (grandparents) + 8 (great-grandparents) + 16 + 32 + 64 + 128 + 256 + 512 + 1024
This total is:
- Generation 0: 1
- Generation 1: 2
- Generation 2: 4
- Generation 3: 8
- Generation 4: 16
- Generation 5: 32
- Generation 6: 64
- Generation 7: 128
- Generation 8: 256
- Generation 9: 512
- Generation 10: 1024
So the total number of ancestors going back 10 generations would be:
1 + 2 + 4 + 8 + 16 + 32 + 64 + 128 + 256 + 512 + 1024 = 2047 ancestors
Since we are only looking for the total number of ancestors excluding yourself (the person), we take:
- Total Ancestors = 2^11 - 1 = 2047 - 1 = 2046
Therefore, the correct answer is B. 2,046 ancestors.