out of 40 people,17 have brothers,22 have sisters and 9 have both.how many people have neither brothers nor sisters
17 - 9 = 8 have only brothers
22 - 9 = 13 have only sisters
9 have both brothers and sisters
40 - 8 - 13 - 9 = 10 have neither.
noice
To solve this problem, we can use the principle of inclusion-exclusion.
Let's denote the number of people who have only brothers as B, the number of people who have only sisters as S, and the number of people who have both brothers and sisters as BS. Additionally, let N represent the number of people who have neither brothers nor sisters.
We are given the following information:
B + BS = 17 (17 people have brothers)
S + BS = 22 (22 people have sisters)
BS = 9 (9 people have both brothers and sisters)
To find N, we need to determine the total number of people (B + S + BS + N) and subtract it from the total number of people, which is 40.
To find B, we subtract the number of people who have sisters and both brothers and sisters from the total number of people who have brothers:
B = 17 - BS = 17 - 9 = 8
To find S, we subtract the number of people who have brothers and both brothers and sisters from the total number of people who have sisters:
S = 22 - BS = 22 - 9 = 13
Finally, to find N, we subtract the total number of people (B + S + BS) from the total number of people (40):
N = 40 - (B + S + BS) = 40 - (8 + 13 + 9) = 40 - 30 = 10
Therefore, there are 10 people who have neither brothers nor sisters.
To find out how many people have neither brothers nor sisters, we need to subtract the number of people who have either a brother or a sister (or both) from the total number of people.
From the given information:
- The number of people with brothers = 17
- The number of people with sisters = 22
- The number of people with both brothers and sisters = 9
To find the number of people who have either a brother or a sister, we can add the number of people with brothers (17) to the number of people with sisters (22) and then subtract the number of people with both brothers and sisters (9):
17 + 22 - 9 = 30
Therefore, there are 30 people who have either a brother or a sister (or both) out of the 40 people in total.
To find the number of people who have neither brothers nor sisters, we subtract this number from the total number of people:
40 - 30 = 10
So, there are 10 people who have neither brothers nor sisters.