Question 31 of 42beginner🔧 ApplyNumerical2 marks

In how many ways can a student choose a programme of 5 courses if 9 courses are available and 2 specific courses are compulsory for every student?

Correct Answer

35 ways

Exercise: EXERCISE 6.4 | Q: 9 | (Page 20)
For More Understanding

Explanation

This is a combination problem where compulsory courses reduce the pool of choices. Since 2 courses are compulsory, they must be included in the programme of 5 courses. The student then needs to choose the remaining 3 courses from the 7 non-compulsory courses (9 total - 2 compulsory). The calculation uses the combination formula nCr = n!/(r!(n-r)!).

Solution Steps

  1. Step 1: Total courses available = 9, Courses to choose = 5, Compulsory courses = 2

  2. Step 2: Since 2 courses are compulsory, they are already fixed in the programme. Remaining courses to choose = 5 - 2 = 3 courses

  3. Step 3: Non-compulsory courses available = 9 - 2 = 7 courses

  4. Step 4: Number of ways to choose 3 courses from 7 courses = ⁷C₃

  5. Step 5: ⁷C₃ = 7!/(3! × 4!) = (7×67 \times 6 × 5)/(3×23 \times 2 × 1) = 210/6 = 35 ways

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