## mathmath333 one year ago The letters of the word ALLAHABAD are rearranged to form new words and put in a dictionary. If the dictionary has only these words and one word on every page in alphabetical order then what is the page number on which the letter LABADALAH comes?

1. mathmath333

\large \color{black}{\begin{align} & \normalsize \text{ The letters of the word ALLAHABAD are rearranged to form }\hspace{.33em}\\~\\ & \normalsize \text{ new words and put in a dictionary. If the dictionary has only}\hspace{.33em}\\~\\ & \normalsize \text{ these words and one word on every page in alphabetical}\hspace{.33em}\\~\\ & \normalsize \text{ order then what is the page number on which the letter }\hspace{.33em}\\~\\ & \normalsize \text{ LABADALAH comes? }\hspace{.33em}\\~\\ \end{align}}

2. Nnesha

sigh.

3. Nnesha

is that the original question or did you change some words ? just asking....

4. mathmath333

It is 100% genuine.

5. Nnesha

okay nvm.it's bank name i guess...

6. kropot72

The total number of pages in the book, with only one new word on each page, is given by: $\large \frac{9!}{4!2!}=7560\ pages$

7. Empty

I can never tell when there's a new one of these questions, for the longest time I just assumed they were always the same "counting question" from looking to the left haha

8. kropot72

The number of pages where the first letter of each new word is L is given by: 8!/4! = 1680 pages. Therefore the number of the first page where the first letter of the new word is L is 7560 - 1680 = page 5880. Now we need to find the number of pages after the word LAAAABDHL that occur until we reach the word LABADALAH.

9. kropot72

The number of new words beginning with LAA is given by 6!/2 = 360. Therefore the number of the first page with new words beginning with LAB is found from: 5880 + 360 + 1 = page 6241. The number of new words where the first letters are LABAA is given by 4! = 24. Therefore the number of the first page with new words beginning with LABAD is found from: 6241 + 24 +1 = page 6266.

10. kropot72

Page 6267 has the word LABADAAHL. Page 6268 has the word LABADAALH. PAGE 6269 has the word LABADAHAL.

11. beginnersmind

@Nnesha "okay nvm.it's bank name i guess..." It's a city in India with a population of over a million.

12. mathmath333

thnks

13. Nnesha

$$\color{blue}{\text{Originally Posted by}}$$ @beginnersmind @Nnesha "okay nvm.it's bank name i guess..." It's a city in India with a population of over a million. $$\color{blue}{\text{End of Quote}}$$ *i guess* i just read the heading https://gyazo.com/8676ed0390348c4c7db93901200ffe25 so i thought it's a bank XD according to wikipedia it supposed to be Ilahabad nd then British changed to Allahabad dun't know why..... it pronounced like Aallahbaad not *bad*

14. Nnesha

sorry mathmath333 ,-, ...

15. mathmath333

I 'the monk" forgives u nesha

16. kropot72

You're welcome :)

17. Nnesha

thank u :P it's *nnesha :D :D