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NDA 2 2024 Maths, question 17

Topic: Algebra

Q17

In how many ways can a student choose (n−2)(n-2) courses out of nn courses if 22 courses are compulsory (n>4)(n>4)?

  1. (a) (n−3)(n−4)(n-3)(n-4)
  2. (b) (n−1)(n−2)(n-1)(n-2)
  3. (c) (n−3)(n−4)/2(n-3)(n-4)/2
  4. (d) (n−2)(n−3)/2(n-2)(n-3)/2Correct answer

Solution.

Answer: (d) (n−2)(n−3)/2(n-2)(n-3)/2

  1. The two compulsory courses are already selected.
  2. Choose n−4 additional courses from the remaining n−2, giving C(n−2,n−4)=C(n−2,2)=(n−2)(n−3)/2.
  3. Equivalently choose the two optional courses to omit.