Answer:
4
Step-by-step explanation:
Let's denote:
- [tex] n(U) [/tex] as the total number of students (40 in this case).
- [tex] n(E) [/tex], [tex] n(M) [/tex], and [tex] n(A) [/tex] as the number of students who passed Economics, Mathematics, and Accounts, respectively.
- [tex] n(ME) [/tex], [tex] n(AE) [/tex], and [tex] n(AM) [/tex] as the number of students who passed both Mathematics and Economics, both Accounts and Economics, and both Mathematics and Accounts, respectively.
- [tex] n(M)only [/tex], [tex] n(A)only [/tex], and [tex] n(E)only [/tex] as the number of students who passed only Mathematics, only Accounts, and only Economics, respectively.
- [tex] r [/tex] as the number of students who failed in all subjects.
Now, we are given the following information:
[tex]\begin{aligned} n(U) & = 40 \\\\n(E) & = 16 \\\\n(M) & = 18 \\\\n(ME) & = 5 \\\\n(A) & = 19 \\\\n(AE) & = 2 \\\\n(M)only & = 6 \\\\n(A)only & = 9 \\\\\end{aligned}[/tex]
From this information, we can find the values of [tex] x [/tex], [tex] y [/tex], and [tex] z [/tex] as follows:
1. For Accounts:
[tex] x + 5 + 2 + 9 = 19 [/tex]
[tex] x + 16 = 19 [/tex]
[tex] x = 19 - 16 [/tex]
[tex] x = 3 [/tex]
2. For Mathematics:
[tex] y + 6 + x + 5 = 18 [/tex]
[tex] y + 6 + 3 + 5 = 18 [/tex]
[tex] y + 14 = 18 [/tex]
[tex] y = 18 - 14 [/tex]
[tex] y = 4 [/tex]
3. For Economics:
[tex] y + x + z = 16 [/tex]
[tex] 4 + 3 + z = 16 [/tex]
[tex] z + 7 = 16 [/tex]
[tex] z = 16 - 7 [/tex]
[tex] z = 9 [/tex]
Now, we need to find the number of students who failed in all subjects ([tex] r [/tex]):
[tex] 40 - r = 6 + 5 + 9 + 2 + 3 + 4 + 7 [/tex]
[tex] 40 - r = 36 [/tex]
[tex] r = 40 - 36 = 4 [/tex]
So, the number of students who failed in all subjects is 4.
