Question

How to find rank of word mother in dictionary without repetition?

Answer 1

(i) Arrange all the alphabets of the word MOTHER in alphabetical order like (E, H, M, O, R, T)

(ii) Now strike off the first letter M from (E, H, M, O, R, T)

(iii) Then count the number of letters before M, and it is equal to 2, which is the coefficient of 5!.

(iv) Then strike off the next letter O (E, H, M, O, R, T)

(v) Then count the number of letters before O and it is equal to 2 which is coefficient of 4!

(vi) Then strike off the next letter T (E, H, M, O, R, T)

(vii) Then count the number of letters before T and it is equal to 3 which is coefficient of 3!

(viii) Then strike off the next letter H (E, H, M, O, R, T)

(ix) Then count the number of letters before H and it is equal to 1 which is coefficient of 2!

(x) Then strike off the next letter E (E, H, M, O, R, T)

(xi) Then count the number of letters before E and it is equal to 0 which is coefficient of 1!

(xii) Then the next word is MOTHER.

So, the rank of the word MOTHER is 2(5!) + 2(4!) +3(3!) + 1(2!) + 0(1!) + 1= 240 + 48+18+2+1 = 309

Hence, the rank of word MOTHER is 309.

Answer 2

I will not directly help you. But I will give steps to you !

Step 1: Write down the letters in alphabetical order.

The correct order is B, I, O, P, P, S

Step 2: Find out the number of words that start with a superior letter

Number of words that start with B will be 5!/2! = 60 (we are dividing by 2 because P is repeating itself)

Step 3: Solve the same problem, without considering the first letter

We have to find the rank of BPSPO

This will be the same as the rank of PSPO

Words above PSPO are the three words starting from O (and ending with PPS, OPSP, OSPP)

Also, PPOS, PPSO, and PSOP will be above PSPO.

=> PSPO will be the 7th word in the list

=> BPSPO will be the 7th word in the list

=> Overall rank of the word IBPSPO is 60 + 7 = 67.