NDA2024MathematicsPermutation and CombinationActual
In how many ways can a student choose (n-2) courses out of n courses if 2 courses are compulsory (n>4) ?
Options
- A(n-3)(n-4)
- B(n-1)(n-2)
- C(n-3)(n-4) 2
- D(n-2)(n-3) 2
Correct answer
D. (n-2)(n-3) 2
Step-by-step solution
We have given that 2 courses are compulsory. Total remaining courses available for selection = n -2 and total remaining courses that can be chosen from ( n-2 ) courses is ( n-2 ) -2=0(n-4) . Thus, required number of ways = ^ (n-2) C _ (n-4) = ( n -2)( n -3) 2