in a class of 50 student,18 offered mathematics, 21 offered chemistry while 16 offered biology, 7 student offered mathematics and biology, 9 student offered chemistry and biology while 5 student offered the three subject combination.
a) find the numbers of student that offered mathematics but offered neither chemistry and biology
b) the number of student who did not offer any of the three subject combination
Draw a Venn diagram if you like, and then recall that
(m+c+b) - (m&c+m&b+b&c) + (m&c&b) = 50 - (none)
now plug in the numbers.
(18+21+16)-(m&c+7+9)+(5) = 50 - (none)
55 - (m&c+16) + 5 = 50-(none)
39+m&c = 50-(none)
m&c = 11-(none)
Since m&c >= 0,
none <= 11
So, as long as no more than 11 people offered nothing, any value will work.
So, if there was a number you forgot to include, plug it in and find the unique solution.
a) To find the number of students who offered mathematics but not chemistry and biology, we need to subtract the number of students who offered the three subject combination and the number of students who offered mathematics and biology from the total number of students who offered mathematics.
Number of students who offered mathematics: 18
Number of students who offered mathematics and biology: 7
Number of students who offered the three subject combination: 5
Number of students who offered mathematics but not chemistry and biology = 18 - 7 - 5 = 6
So, 6 students offered mathematics but not chemistry and biology.
b) To find the number of students who did not offer any of the three subject combinations, we need to find the number of students who offered none of the three subjects.
Total number of students = 50
Number of students who offered mathematics = 18
Number of students who offered chemistry = 21
Number of students who offered biology = 16
We can find the number of students who did not offer any of the three subject combinations by subtracting the sum of all the students who offered the three subjects from the total number of students.
Number of students who offered none of the three subject combinations = 50 - (18 + 21 + 16 - 5) = 50 - 50 = 0
Therefore, there are 0 students who did not offer any of the three subject combinations.
To find the number of students that offered mathematics but did not offer chemistry or biology, we need to subtract the number of students who offered both mathematics and either chemistry or biology, from the total number of students who offered mathematics.
a) Number of students that offered mathematics but did not offer chemistry or biology:
Total number of students who offered mathematics = 18
Now, let's find the students who offered both mathematics and either chemistry or biology:
Number of students who offered mathematics and biology = 7
Number of students who offered mathematics and chemistry = 5
Number of students who offered all three subjects = 5
So, the number of students who offered both mathematics and either chemistry or biology can be determined by adding the number of students who offered mathematics and biology (7) and the number of students who offered mathematics and chemistry (5), and then subtracting the number of students who offered all three subjects (5).
Number of students who offered both mathematics and either chemistry or biology = 7 + 5 - 5 = 7
Therefore, the number of students who offered mathematics but did not offer chemistry or biology is:
18 - (7 + 5 - 5) = 11
b) To find the number of students who did not offer any of the three subject combinations, we need to subtract the sum of students who offered mathematics, chemistry, biology, or any combination of these subjects from the total number of students (50).
Number of students who offered mathematics = 18
Number of students who offered chemistry = 21
Number of students who offered biology = 16
Number of students who offered both mathematics and chemistry = 5
Number of students who offered both mathematics and biology = 7
Number of students who offered both chemistry and biology = 9
Number of students who offered all three subjects = 5
Total number of students who did not offer any of the three subject combinations:
50 - (18 + 21 + 16 - (5 + 7 + 9) + 5) = 50 - (60 - 21) = 50 - 39 = 11
Therefore, the number of students who did not offer any of the three subject combinations is 11.