In an assembly after Tet Holiday, there are $81$ primary students, $67$ secondary students and $53$ high school students. The principal calls students randomly by name to give red envelopes. At least how many students does the principal need to call to ensure that $5$ primary students and $7$ secondary students receive the gifts?

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Q. In an assembly after Tet Holiday, there are

81

primary students,

67

secondary students and

53

high school students. The principal calls students randomly by name to give red envelopes. At least how many students does the principal need to call to ensure that

5

primary students and

7

secondary students receive the gifts?

Calculate Primary Students: We need to ensure that $5$ primary students receive gifts. Since there are $81$ primary students, the worst-case scenario is that the principal calls all of them except $4$ (to ensure that at least $5$ get the gift). $\newline$ Calculation: $81 - 4 = 77$
Calculate Secondary Students: Similarly, to ensure that $7$ secondary students receive gifts, the principal might need to call all secondary students except $6$ . $\newline$ Calculation: $67 - 6 = 61$
High School Students: For high school students, there is no minimum number specified, so we do not need to include them in our calculation for the minimum number of students the principal needs to call.
Total Number of Students: Now, we add the number of primary and secondary students the principal needs to call to ensure the minimum number of students receiving gifts. $\newline$ Calculation: $77$ (primary students) + $61$ (secondary students) = $138$