Dedicated to all moms in the world

Probability Level 3

If a dictionary is formed using all possible arrangements of the letters of the word "MOTHER", then the rank of the word "MOTHER" in the dictionary will be?

Details and Assumptions

Here rank means at what number the word comes in the dictionary made of all possible arrangements the letters of that particular word.
Like a normal dictionary, the words are alphabetized from A to Z.

Try more combinatorics problems.

The answer is 309.

1 solution

Discussions for this problem are now closed

Naman Kapoor
Oct 16, 2014

Firstly we'll arrange it in alphabetical order i.e MOTHER-EHMORT then we will fill the words until the desired alphabet comes E_ _ _ _ _ ....M_ _ _ _ _ SINCE 5 places r empty we will use 5! And repeat it till we get the word MOTHER after solving we will get 5!+5!+4!+4!+3!+3!+3!+2!+1! Solving it we will get 309

@Yogesh Ghadge I'll explain it for you.

What we're doing is listing all the arrangements that came before the

word 'MOTHER'.

Since E came first in the dictionary and there's 5! way to arrange 5

different letters, there's 5! arrangements that begins with letter E

and came before MOTHER.

Next, we do this again with the next letters , H.

So we'll get....

E_ _ _ _ _ ---> 5!

H_ _ _ _ _ ---> 5!

ME _ _ _ _ ---> 4!

MH _ _ _ _----> 4!

MOE _ _ _ ----> 3!

MOH_ _ _ ----> 3!

MOR_ _ _ -----> 3!

MOTE_ _ ---->2!

MOTHER

So we add them up and get 308.

There's 308 arrangements that came before the word MOTHER so

the RANK of the word is 309.

I got it wrong because at first I accidentally thought T came before R.

(stupid me :)

Peter Bishop - 6 years, 7 months ago

Done is the same way :-)

Bhargav Upadhyay - 6 years, 3 months ago

Dedicated to all moms in the world

Try more combinatorics problems.

The answer is 309.

1 solution

Discussions for this problem are now closed

0 pending reports