The letters of the word ‘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

Question

Smart Achievers · Accepted Answer

(1)

$\begin{matrix} M & A & N & K & I & N & D \end{matrix}$

$(\frac{4 \times 6!}{2!}) + (5! \times 0) + (\frac{4! \times 3}{2!}) + (3! \times 2) + (2! \times 1) + (1! \times 1) + (0! \times 0) = 1492$

$\Rightarrow 1440 + 36 + 12 + 4 = 1492$

Solution

Q.
The letters of the word ‘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

1 1492

2 1493

3 1490

4 1491

Ans.
(1)

$\begin{matrix} M & A & N & K & I & N & D \end{matrix}$

$(\frac{4 \times 6!}{2!}) + (5! \times 0) + (\frac{4! \times 3}{2!}) + (3! \times 2) + (2! \times 1) + (1! \times 1) + (0! \times 0) = 1492$

$\Rightarrow 1440 + 36 + 12 + 4 = 1492$

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