Question

The number of permutations of $4$ letters from the letters of word ${}^{\prime }KOLKAT{A}^{\prime }$, is

• A. $210$
• B. $270$
• C. $354$
• D. $436$

Answer 1

The correct option is A $210$

According to the question, the word ${}^{\prime }KOLKAT{A}^{\prime }$ has $7$ letters among which there are $2K$ and $2A$

Thus the permutation of any $4$ letters among these $7$ can be expressed as

$P(7,4)=\frac{7!}{\left(7-4\right)!\times \left(2!\times 2!\right)}$ using formula $p\left(n,r\right)=\frac{n!}{\left(n-r\right)!}$

$=\frac{7\times 6\times 5\times 4}{2\times 2}$

$=210$

Hence, $A$ is the correct answer.