Question

How many $4$-letter words, with or without meaning, can be formed out of the letters of the word, 'LOGARITHMS', if repetition of letters is not allowed?

• A. $5040$
• B. $1000$
• C. $2500$
• D. $2060$

Answer 1

The correct option is A $5040$

There are $10$ letters in the word 'LOGARITHMS'.
So, the number of $4$-letter word$=$Number of arrangements of $10$ letters, taken $4$ at a time
$=$ ${}^{10}{P}_4=5040$.