Question

Find the number of words which can be made using all the letters of the word IMAGE. If these words are written as in a dictionary, what will be the rank of MAGIE?

(a) 97

(b) 98

(c) 99

(d) 100

I had been asked this question in quiz.

I need to ask this question from Permutations-2 in section Permutations and Combinations of Mathematics – Class 11

Answer 1

Right answer is (c) 99

Easiest explanation: Words starting with letter A comes first in dictionary. Starting with A, number of words = 4! = 24. Starting with E, number of words = 4! = 24. Starting with I, number of words = 4! = 24. Starting with G, number of words = 4! = 24. Since our word also start with M so, we have to consider one more letter i.e. MA. Since our word also start with MA so, we have to consider one more letter i.e. MAE. Starting with MAE, number of words = 2! = 2. Since our word also start with MAG so, we have to consider one more letter i.e. MAGE. Starting with MAGE, only one letter i.e. MAGEI. After this, MAGIE comes. Total number of words before MAGIE = 24 + 24 + 24 + 24 + 2 = 98. So, rank of MAGIE is 99.