Find the number of 4 letter words that can be formed using the letters of the word RAMANA'.

The word has 6 letters of which 3 are alike and the rest are different 
The letters are R, M, N, A, A, A 
The number of 4 letter words which are all different = 4! =24 
The number of 4 letter words of which 3 are alike and one different i.e., using 
AAAR, AAAM, AAAN = $=\frac{4}{3}\times 3=12$
The number of 4 letter words of which 2 are alike and the rest are different 
i.e., using AARM, AARN, AAMN $=\frac{4}{2}\times 3=36$ 
Required number of arrangements $=24+12+36=72$