The number of 5-letter words that can be formed by using the letters of the word SARANAM is

Step-by-step solution

There are 7 letters in the word 'SARANAM' of which there are 3 ~A and all other are distinct. The five letter words may consist of (i) all different letters (using S, A, R, N, M) Required words =5 !=120 (ii) 2 alike and other different (using 2 ~A and 3 other) Required words = ^4 C₃ 5 ! 2 ! =4 120 2 =240 (iii) 3 alike and other different (using 3A and 2 other) Required words = ^4 C₂ 5 ! 3 ! = 4 3 2 1 120 6 =120 Total words =120+240+120=480