In how many ways can the letters of the word 'ALLEN' be arranged? Also, find its rank if all these words are arranged as they are in dictionary.

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Solution

ALLEN
$\Rightarrow$ ways can be letters arranged
$= 5!$
$= 120$
Rank $A - - - - 4!$
$A E - - - 3!$
$A E N - - \frac{1}{4! + 3! + 1}$
$= 24 + 6 + 1$
$= 31$
$\sqrt{1.5625}$
$= \sqrt{\frac{15625}{10000}}$

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In how many ways can the letters of the word 'ALLEN' be arranged? Also, find its rank if all these words are arranged as they are in dictionary.

ALLEN ⇒ ways can be letters arranged =5!=120Rank A−−−−4!AE−−−3! AEN−−14!+3!+1=24+6+1=31√1.5625=√1562510000

ALLEN
$\Rightarrow$ ways can be letters arranged
$= 5!$
$= 120$
Rank $A - - - - 4!$
$A E - - - 3!$
$A E N - - \frac{1}{4! + 3! + 1}$
$= 24 + 6 + 1$
$= 31$
$\sqrt{1.5625}$
$= \sqrt{\frac{15625}{10000}}$