The letters of the work ‘MANKIND’ are written in all possible orders and arranged in serial order as in an English dictionary. Then the serial number of the word ‘MANKIND’ is ______.
The letters of the work ‘MANKIND’ are written in all possible orders and arranged in serial order as in an English dictionary. Then the serial number of the word ‘MANKIND’ is ______.
Correct Answer: 1492
Solution and Explanation
Arranging letters in alphabetical order A D I K M N N to find rank of MANKIND and making arrangements of a dictionary we get
A ………….\(\frac{6!}{2!}\)=360
D …………. 360
I …………. 360
K …………. 360
M A D ………….\(\frac{4!}{2!}\)=12
M A I ………….12
M A K ………… 12
M A N D …………. 3! = 6
M A N I …………. 6
M A N K D …………. 2
M A N K I D …………. 1
M A N K I N D …………. 1
∴ Rank of MANKIND = 1440 + 36 + 12 + 2 + 2
= 1492
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Concepts Used:
Permutations and Combinations
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Permutation is the method or the act of arranging members of a set into an order or a sequence.
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Combination:
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