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 = 𝑛!/𝑝1!𝑝2!𝑝3!
Remaining letters = n = 10
Since, 2I, 2N
∴ p1 = 2, p2 = 2
Words starting with letter A
Since letter are repeating,
Hence we use this formula = 𝑛!/𝑝1!𝑝2!𝑝3!
Remaining letters = n = 10
Since, 2I, 2N
∴ p1 = 2, p2 = 2
Number of words formed by there letters = 𝑛!/𝑝1!𝑝2!
= 10!/2!2!
= 907200
Thus,
Words in the list before the word starting with E
= Words starting with letter A
= 907200

Davneet Singh has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 13 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.

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