Question

The number of ways in which ten candidates $A_1,A_2,A_3......A_{10}$ can be ranked if $A_1$ and $A_2$ are next to each other is

• A. 2!.11!
• B. 2!.10!
• C. 2!.9!
• D. 2!.8!

Answer 1

The correct option is C 2!.9!

Consider $A_1$,$A_2$ as one entity so that there are 10-2+1= 9 candidates which can be arranged amongst themselves in 9! ways.
But these two $A_1$ and $A_2$ can be arranged among themselves in 2! =2 ways.
Hence the number of ways $A_1$ and $A_2$ are together is 2!.9! ways.