JEE PYQ: Permutation And Combination Question 15
Question 15 - 2020 (02 Sep Shift 1)
If the letters of the word ‘MOTHER’ be permuted and all the words so formed (with or without meaning) be listed as in a dictionary, then the position of the word ‘MOTHER’ is ______.
Show Answer
Answer: 309
Solution
M O T H E R. Alphabetical order: E H M O R T. Words starting with E: $5! = 120$. Starting with H: $5! = 120$. Starting with ME: $4! = 24$. Starting with MH: $4! = 24$. Starting with MOE: $3! = 6$. Starting with MOH: $3! = 6$. Starting with MOR: $3! = 6$. Starting with MOTE: $2! = 2$. Starting with MOTH: next is MOTHER = 1. Position $= 120 + 120 + 24 + 24 + 6 + 6 + 6 + 2 + 1 = 309$.
BETA
