Q144 / 240 · KCET 2026 · Mathematics
How many ways can you arrange all the letters and numbers in "KCET 2025" which start with K and end with $5$?
- A$720$
- Correct answerB$360$
- C$120$
- D$180$
Solution
The given alphanumeric string is KCET 2025.
The letters and numbers present are K, C, E, T, $2$, $0$, $2$, $5$.
The total number of characters to be arranged is $8$.
The first position is fixed for K and the last position is fixed for $5$.
The remaining $6$ positions are to be filled by the remaining $6$ characters: C, E, T, $2$, $0$, $2$.
Among these $6$ characters, the digit $2$ is repeated twice.
The number of ways to arrange these $6$ characters is $\dfrac{6!}{2!}$.
$\dfrac{6!}{2!} = \dfrac{720}{2} = 360$
Answer: $360$
The letters and numbers present are K, C, E, T, $2$, $0$, $2$, $5$.
The total number of characters to be arranged is $8$.
The first position is fixed for K and the last position is fixed for $5$.
The remaining $6$ positions are to be filled by the remaining $6$ characters: C, E, T, $2$, $0$, $2$.
Among these $6$ characters, the digit $2$ is repeated twice.
The number of ways to arrange these $6$ characters is $\dfrac{6!}{2!}$.
$\dfrac{6!}{2!} = \dfrac{720}{2} = 360$
Answer: $360$
Hence, the correct answer is option: 'B'.