If the different permutations of all the letter of the word EXAMINATION are listed as in a dictionary, how many words are there in this list before the first word starting with E?

Solution:

In the dictionary, words are arranged in alphabetical order.

The words before the first word starting with E are the words with starting letters like A, B, C, D.

But there is no B, C, D in the given word.

Words before the first word starting with E = Words starting with the letter A.

Finding the number of words starting with A:

The total number of letters = 11.

The first position of the word is filled with A.

So the remaining 10 positions should be filled with the remaining 10 letters. Note that there are  2 I's and  2 N's in the given word.

We know that the number of arrangements (permutations) that can be made out of n things out of which there are p, q, r, ... number of repetitions = n! / [p! q! r! ...]. Thus, the total no. of words starting with A = 10! / (2! 2!) = 907200.

Thus, the total no. of words before the first word starting with E = 907200

NCERT Solutions Class 11 Maths Chapter 7 Exercise ME Question 4

If the different permutations of all the letter of the word EXAMINATION are listed as in a dictionary, how many words are there in this list before the first word starting with E?

Summary:

If the different permutations of all the letters of the word EXAMINATION are listed as in a dictionary, then the number of words that are there in this list before the first word starting with E is 907200