Question

How many integral solutions are there for the equation A+B+C = 10 where $A\ge 1,B\ge 2,C\ge 3$?

• A. ⁵C₂
• B. ⁶C₂
• C. ¹²C₂
• D. ⁸C₂
• E. None of these

Answer 1

The correct option is B ⁶C₂

This is a question based on $S\stackrel{‘}{a}D$ with a varying lower limit.

Take out 1+2+3=6 from the RHS. Equation changes to

A+B+C = 4. Answer will the arrangement of 4 zeroes and 2 ones = ${}^6{C}_2$