Question

The number of $4$ letter word that can be made with the letter of the word $COMBINATION$ is

• A. $2354$
• B. $2454$
• C. $1454$
• D. None of these

Answer 1

Answer: (B)

$2454$

The word COMBINATION has 2I,2O,2N and C,M,B,A,T
That is :$IIOONNCMBAT$
The 4 letter word can be formed in following ways:
All different word=$\left(\begin{array}{c}8\\ 4\end{array}\right)\times 4!=1680$
2 alike 2 different=$\left(\begin{array}{c}3\\ 1\end{array}\right)\times \left(\begin{array}{c}7\\ 2\end{array}\right)\times \frac{4!}{2!}=756$
2 alike and 2 other alike=$\left(\begin{array}{c}3\\ 2\end{array}\right)\times \frac{4!}{2!\times 2!}=18$
Therefore, the total number of 4 lettered words $=(1680+756+18)=2454$
Hence, option 'B' is correct.