Question

In how many unique ways can the seven letters in the word MINIMUM be arranged, if all the letters are used each time

Answer 1

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

$\frac{n!}{n_{1}! n_{2}!..n_{k}! }$

where, n = $n_{1} +n_{2} +n_{3} ...+n_{k}$

$n_{1}$ is objects of one type

$n_{2}$ is the objects of two types

$n_{k}$ 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.

Find out more information about number of ways and permuations here:

brainly.com/question/15609044

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