Question

How many different words can be formed by using all the letters of the word INSTITUTE?

• A. 9!
• B. $\frac{9!}{2!}$
• C. $\frac{9!}{3!}$
• D. $\frac{9!}{(3!\times 2!)}$

Answer 1

The correct option is D $\frac{9!}{(3!\times 2!)}$

Total number of letters = 9. So, the number of arrangements possible = 9!
But, The letters I and T are repeated 2 and 3 times respectively.
Hence, the total number of arrangements possible with the letters of the word INSTITUTE $=\frac{9!}{(3!\times 2!)}$