Question

How many natural number solutions are there for the equation, A+B+C = 100?

• A. ⁹⁹C₂
• B. ⁹⁹C₃
• C. ¹⁰¹C₂
• D. ⁹⁹C₉₉

Answer 1

The correct option is A

⁹⁹C₂

Natural number solutions means each of A,B and C can take a value ≥ 1

This is a Similar to Different question, with a lower limit condition. (Refer ebooklet for indepth explanation)

To take care of the condition, that we are dealing with natural numbers,

give A,B &C 1 initially

(A+1)+(B+1)+(C+1)=100

Thus, this reduces to A+B+C=97.

This question is now based on arrangement of 97 zeroes and 2 ones=${}^{99}$C${}_2$

The answer is ${}^{99}$C${}_2$ which is option (a)