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. 40
B. 400
C. 5040
D. 2520

Hint: Calculate the alphabet of the letters ‘LOGARITHMS’ and keep in mind that no letter can be used twice, also count those letters which are repeated in the word ‘LOGARITHMS’.

Complete step by step solution:
The word ‘LOGARITHMS’ is given and we have to form a word of 4 letters and repetition is not allowed.
Total letters in ‘LOGARITHMS’ are 10 letters.
A word of 4 letters is to be formed out of these 10 letters and repetitions is not allowed.
In the place of 1st position, we have 10 letters and one is to be fixed.
In the place of 2nd position, we have left 9 letters and one is to be fixed.
In the place of 3rd position, we have left 8 letters and one is to be fixed.
In the place of 4th position, we have left 7 letters and one is to be fixed.
Hence, the total number of possibilities can be found by multiplying all the obtained numbers of letters.
$
  {\text{ = 10}} \times {\text{9}} \times {\text{8}} \times {\text{7}} \\
  {\text{ = 5040}} \\
$
Therefore, $5040$ words can be formed.
Hence the correct option is C.

Note: fixed one letter at a position and keep in mind that repetition is not allowed therefore this fixed letter cannot be used again and that is why we have left one less letter for the next position.