The number of unique ways or permuations to arrange the seven letters in MINIMUM is all the letters are used each time is 420.
According to the given question.
We have a word MINIMUM.
Here, there are 7 letters in "MINIMUM" .
Now, in Minimum the number of letters which are repeated and which are not.
M = 3 times
I = 2 times
N = 1 time
U = 1 time
As, we all know if there is no repetitions in a word which is made of n letters, then we can arrange it by n! ways.
But if there is repetition, we use formula
where, n =
is objects of one type
is the objects of two types
is the objects of k types
Thereofore, the number of unique ways or permuations to arrange the seven letters in MINIMUM is all the letters are used each time
= 7!/ 3!2!
= 7(6)(5)(4)(3!)/3!(2)(1)
= 7(3)(5)(4)
= 420
Hence, the number of unique ways or permuations to arrange the seven letters in MINIMUM is all the letters are used each time is 420.
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