Question

How many $4$ letters words can be formed out of the letters of the word LOGARITHMS, if repetition of letters is not allowed?

• A. $5000$
• B. $5040$
• C. $5020$
• D. $5010$

Answer 1

Answer: (B)

$5040$

The word LOGARITHMS contains $10$ different letters.
Therefore, the number of required words
$=$ Number of arrangements of $10$ letters taken $4$ at a time
$={{}^{10}P}_4=10\times 9\times 8\times 7=5040$