a) Total students = 75, n(P H) = 75, n(P H) = 10, n(P) : n(H) = 2 : 3. Find n(P) and n(H).

10. a) Given: Total students = 75 Students who like picnic (P) or hiking (H) or both, n(P H) = 75. Students who like both activities, n(P H) = 10. The ratio of the number of students who like picnic to those who like hiking is n(P) : n(H) = 2 : 3. Step 1: Find the values of n(P) and n(H). We know the formula for the union of two sets: $n(P H) = n(P) + n(H) - n(P