Question

The number of 4 letter words that can be formed using the letters of the word COMBINATION is

• A. $2436$
• B. $2454$
• C. $1698$
• D. $498$

Answer 1

The correct option is B $2454$

We have:
C O M B I N A T I O N
We need to select 4 letters and arrange:
Case 1: All distinct: ${}^8{P}_4=1680$
Case 2: One letter repeated twice: Either O, I, N can repeat: ${}^3{C}_1{\times }^7{C}_2\times \frac{4!}{2!}=756$
Case 3: Two letters repeated twice: O and I, OR O and N, OR I and N can repeat: $3\times \frac{4!}{2!2!}=18$
Hence, the answer = $1680+756+18=2454$