Question

How many four letter words with or without meaning that can be formed by using the letters of the word ${}^{\prime }LOGARITHM{S}^{\prime }$ such that the letter $R$ is always included? ( repetition is not allowed )

• A. $12096$
• B. $2458$
• C. $1296$
• D. $2240$

Answer 1

The correct option is A $12096$

Word : LOGARITHMS

Number of letters $=10$

Four letter word to be formed $R$ always included

we need to select three more letters number of ways of selecting

${\Rightarrow }^9{P}_3\Rightarrow 9\times 8\times 7$

$\Rightarrow 504$ Ways

Now we have four letters

Integral arrangement $=4!=24$

Total possible four lettered word

$\Rightarrow 504\times 24\Rightarrow 12096$