permutations and combinations

The letters of the word "sachin" are arranged in all possible ways as a 6 letter word and that words are made as dictionary. then what will be the positions of the word "sachin" in that dictionary . [for more problems and solutions contact my e-mail "sudokusubramanyam@gmail.com"]


The answer is 601.

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1 solution

Vaibhav Prasad
Mar 28, 2015

First we will have to arrange the digits in alphabetical order as follows : a , c , h , i , n , s a, c, h, i, n, s

Then, the number of words that can be formed with...

a a as first letter is = 5 ! = 120 5! = 120

c c as first letter is = 5 ! = 120 5! = 120

h h as first letter is = 5 ! = 120 5! = 120

i i as first letter is = 5 ! = 120 5! = 120

n n as first letter is = 5 ! = 120 5! = 120

The total now is 600 600

Then we will have s s as first letter, which we want. After s s , the first letter that we will get is a a , which we want. After a a , the first letter that we will get c c , which we want. After c c , the first letter that we will get is h h , which we want. After h h , the first letter that we will get i i , which we want. After i i , the first letter that we will get n n , which we want.

Thus we can see that s a c h i n sachin is the first word after 600 600 words. Thus it's position is 601 \boxed {601}

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