Question

If letters of the word ${}^{\prime }GYRATIO{N}^{\prime }$ is permuted in all possible ways,
a)How many words begin with $G$
b)How many words start with $G$ and end with $T$

• A. $7!,6!$
• B. $8!,7!$
• C. $7!,7!$
• D. $6!,7!$

Answer 1

The correct option is A $7!,6!$

a)If we fix the first place as $G$, the remaining $7$ letters can be permuted in $7!$ ways
So required answer $=7!$
b)Now if we fix both first and last places, remaining $6$ letters can be permuted in $6!$ ways
So required answer $=6!$