Question

Mr. A has $x$ children by his first wife and Ms. B has $x+1$ children by her first husband. They marry and have $x$ children of their own. The whole family has 10 children. Assuming that two children of the same parents do not fight, the maximum number of fights that can take place among the children is

• A. $33$
• B. $35$
• C. $38$
• D. $34$

Answer 1

The correct option is A $33$

Total number of children in the house is $=x+x+1+x=10$ (given) $\Rightarrow x=3$
Hence maximum number of fights is,
${=}^3{C}_1{.}^4{C}_1{+}^4{C}_1{.}^3{C}_1{+}^3{C}_1{.}^3{C}_1=12+12+9=33$