Misc 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?
In dictionary, words are given alphabetically
We need to find words starting before E i.e. starting with A,B,C or D
In EXAMINATION, there is no B,C or D ,hence words should start with A
Words in the list before the word starting with E
= Words starting with letter A
Words starting with letter A
Since letter are repeating,
Hence we use this formula = π!/π1!π2!π3!
Remaining letters = n = 10
Since, 2I, 2N
β΄ p1 = 2, p2 = 2
Words starting with letter A
Since letter are repeating,
Hence we use this formula = π!/π1!π2!π3!
Remaining letters = n = 10
Since, 2I, 2N
β΄ p1 = 2, p2 = 2
Number of words formed by there letters = π!/π1!π2!
= 10!/2!2!
= 907200
Thus,
Words in the list before the word starting with E
= Words starting with letter A
= 907200

Made by

Davneet Singh

Davneet Singh is a graduate from Indian Institute of Technology, Kanpur. He has been teaching from the past 12 years. He provides courses for Maths and Science at Teachoo.