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

The given word RAMANA has 6 letters in which there are 3 A’s are alike and rest are different
Case (i):-
All different letters R, A, M, N

No. of 4 letters words formed = 4! = 24

Case (ii):-
Two like letters A, A and two out of R, M, N The two different letters can be chosen from 3 letters in ³C₂ ways

$\therefore$ No. of 4 letters words formed${=}^3{C}_2\times \frac{4!}{2!}=36$

Case (iii):-
three like letter A, A, A and one out of R, M, N one letter can be chosen from 3 different letters in ³C₁ways

$\therefore$No. of 4 letters words formed ${=}^3{C}_1\times \frac{4!}{3!}=12$

$\therefore$Total no. of 4 letters words formed from the word RAMANA = 24 + 36 + 12 = 72