Question

A party of $9$ persons are to travel in two vehicles, one of which will not hold more than $7$ and other not more than $4.$ The number of ways the party can travel is

• A. $120$
• B. $220$
• C. $236$
• D. $246$

Answer 1

The correct option is D $246$

Vehicle $1$ and Vehicle $2$ can hold $(7,2),(6,3)(5,4)$ Persons respectively.
So, required number of ways $={{}^9{C}_7}^2{C}_2+{{}^9{C}_6}^3{C}_3+{{}^9{C}_5}^4{C}_4=246$