In an examination 18 candidates passed mathematics 17 candidates passed physics 11 candidates passed both and 1 failed both find the number that passed physics and the total candidates
Let's call the number of candidates that passed physics as P and the total number of candidates as T.
According to the problem, there are 18 candidates that passed mathematics, 17 candidates that passed physics, and 11 candidates that passed both. We also know that 1 candidate failed both.
We can use the principle of inclusion-exclusion to find the number of candidates that passed physics.
Total number of candidates that passed:
= Number of candidates that passed mathematics + Number of candidates that passed physics - Number of candidates that passed both
= 18 + 17 - 11
= 24
So, the number of candidates that passed physics is 24.
To find the total number of candidates, we add the number of candidates that passed physics with the number of candidates that failed both.
Total number of candidates = Number of candidates that passed physics + Number of candidates that failed both
= 24 + 1
= 25
Therefore, the total number of candidates is 25.
To find the number of candidates who passed physics and the total number of candidates, we can use the principle of inclusion-exclusion.
Let's denote the total number of candidates who passed physics as "P" and the total number of candidates who passed mathematics as "M". The total number of candidates in the examination can be denoted as "T".
We are given that 18 candidates passed mathematics, 17 candidates passed physics, 11 candidates passed both, and 1 candidate failed both.
Using the principle of inclusion-exclusion, we can calculate the values of P and T.
P = M + 17 - 11 (Adding the number of candidates who passed mathematics and the number who passed physics, then subtracting the number who passed both since they were counted twice)
P = M + 6
T = M + P - 11 + 1 (Adding the number of candidates who passed mathematics and the number who passed physics, then subtracting the number who passed both since they were counted twice, and finally adding the 1 candidate who failed both)
T = M + P - 10
Since we don't have the exact value of M, we cannot determine the specific number of candidates who passed physics or the total number of candidates without additional information.
To find the number of candidates who passed physics and the total number of candidates, we can use the principle of inclusion-exclusion.
Let's denote:
- P as the number of candidates who passed physics,
- M as the number of candidates who passed mathematics,
- P∩M as the number of candidates who passed both physics and mathematics,
- N as the total number of candidates.
Using the given information:
- P = 17 (number of candidates who passed physics)
- M = 18 (number of candidates who passed mathematics)
- P∩M = 11 (number of candidates who passed both physics and mathematics)
- 1 candidate failed both.
We can then use the principle of inclusion-exclusion to find N, the total number of candidates.
The principle of inclusion-exclusion states:
N = P + M - P∩M + Neither
In this case, "Neither" refers to the number of candidates who failed both mathematics and physics, which is given as 1.
Substituting the given values into the formula:
N = 17 + 18 - 11 + 1
N = 17 + 18 - 11 + 1
N = 35 - 11 + 1
N = 24 + 1
N = 25
So, the number of candidates who passed physics is 17, and the total number of candidates is 25.