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.
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.
Comments
Post a Comment
Share this to your friends