Problem Solving : Permutation and combination Problem 2: If the letter of the word VERMA are arranged in all possible ways and these words are written out as in a dictionary form, then what is the rank of the word VERMA is ?

If the letter of the word VERMA are arranged in all possible ways and these words are written out as in a dictionary form, then what is the rank of the word VERMA is ?

Solution:

so the word VERMA letters of V, E, R, M, A

In alphabetical order A, E, M, R, V

So the number of words begin with A = 4! (leave A and consider remaining letters E, M, R, V)
and the number of words begin with E= 4! (leave A and consider remaining letters A, M, R, V)
and the number of words begin with M = 4! (leave A and consider remaining letters E, A, R, V)
and the number of words begin with R = 4! (leave A and consider remaining letters E, M, A, V)
after the word begins with V so here after consider two or more words combinations

So the number of words begin with VA = 3! (leave v and A and consider remaining 3 letters E,M, R)
VE becomes next character after VA set so below are the dictionary arrangement goes

1) VEAMR
2) VEARM
3) VEMAR
4) VEMRA
5) VERAM

finally 6) VERMA

Hence the Rank = 4! + 4! + 4! + 4! + 3! + 6 = 96 + 6+ 6 =108th Rank


Rank of the word VERMA is 108.