Find the number of 4-letter words. with or without meaning, which can be formed out of the letters of the word, 'NOSE' , when :
(i) the repetition of the leters is not allowed,
(ii) the repetition of the letters is allowed.

Explanation

Case (i) When the repetition of the letters is not allowed:
In this case, the total number of words is the same as the number of ways of filling 4 places `square square square square` by 4 different letters chosen from N, O, S, E.
The first place can be filled by any of the 4 letters. Thus, there are 4 ways of filling the first place. Since the repetition of letters is not allowed, so the second place can be filled by any of the remaining 3 letters in 3 different ways.
Following it, the third place can be filled by any of the two remaining letters in 2 different ways. And, the fourth palce can be filled by the remaining one letter in 1 way.
So, by the fundamental principle of multiplication, the required number of 4 -letter words`=(4xx3xx2xx1)=24`.
Hence, required number of words `=24`.
Case (ii) When the repetition of the letters is allowed:
In this case, each of the four different places can be filled in succession in 4 different ways.
So, the required number of 4 -letter words `=(4xx4xx4xx4)=256.`