By signing in you confirm you are 18 or older, or have your parent’s or guardian’s consent.

NDA 1 2025 Maths, question 19

Topic: Algebra

Q19

What is the number of positive integer solutions of x+y+z=5x + y + z = 5?

  1. (a) 3
  2. (b) 5
  3. (c) 6Correct answer
  4. (d) 9

Solution.

Answer: (c) 6

  1. Put x=X+1x = X + 1, y=Y+1y = Y + 1, z=Z+1z = Z + 1, where X,Y,Z≥0X,Y,Z \geq 0.
  2. Then X+Y+Z=2X + Y + Z = 2.
  3. By stars and bars, the number is (2+3−13−1)=(42)=6\binom{2 + 3 - 1}{3 - 1} = \binom{4}{2} = 6.