The letters of the word 'MANKIND' are written in all possible orders and arranged in serial order as in an English dictionary. Then the serial number of the word 'MANKIND' is _____ .

Step-by-step solution

M A N K I N D Arranging the letters alphabetically, we get ADIKMNN When the word starts with any of the letters A/D/I/K, the number of possibilities = 6 ! 2 ! × 4 = 1440 Now when the word starts with MA, then the number of possibilities = 4 ! 2 ! × 3 = 36 Now when the word starts with MAN, then the number of possibilities = 3 ! × 2 = 12 Now when the word starts with MANK, then the number of possibilities = 4 Hence, rank of the work MANKIND is 1492