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
Permutation:
Permutation is the method or the act of arranging members of a set into an order or a sequence.
- In the process of rearranging the numbers, subsets of sets are created to determine all possible arrangement sequences of a single data point.
- A permutation is used in many events of daily life. It is used for a list of data where the data order matters.
Combination:
Combination is the method of forming subsets by selecting data from a larger set in a way that the selection order does not matter.
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- The combination is used for a group of data where the order of data does not matter.