Find the number of words formed (may be meaningless) by using all the

Question:

Find the number of words formed (may be meaningless) by using all the letters of the word ‘EQUATION’, using each letter exactly once.

Solution:

There are 8 alphabets in the word EQUATION.

Formula:

Number of permutations of $n$ distinct objects among $r$ different places, where repetition is not allowed, is

$P(n, r)=n ! /(n-r) !$

Therefore, a permutation of 8 different objects in 8 places is

$P(8,8)=\frac{8 !}{(8-8) !}=\frac{8 !}{0 !}=\frac{40320}{1}=40320$

Hence there are 40320 words formed.

 

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