Question

How many four letter words with or without meaning can be formed out of the letters of the word ${}^{\prime }LOGARITHM{S}^{\prime }$ if repetition of letters is not allowed?

• A. $40$
• B. $360$
• C. $5040$
• D. none of these

Answer 1

The correct option is C $5040$

We have to form $4$ lettered words from the given $10$ letters $L,O,G,A,R,I,T,H,M,S$

Total words $={}^{10}{C}_4\times 4!$

$\Rightarrow$ ${}^{10}{C}_4=\frac{10!}{6!}$

$=5040.$

Hence, the answer is $5040.$