Question

A popular website requires users to create a password consisting of digits only. If no digit may be repeated and each password must be at least 9 digits long, how many passwords are possible

Answer 1

Answer:

I would say about a billion because numbers can be put in any combination

Step-by-step explanation:

EXAMPLES:

012345678

023456781

034567812

045678912

123456780

234567801

345678012

456780123

567801234

678012345

780123456

801234567

123456789

234567891

345678912

456789123

567891234

678912345

789123456

891234567

912345678

Answer 2

There are 3,628,800 possible ways to create passwords .

What is permutation?

Permutations are different ways of arranging objects in a definite order. It can also be expressed as the rearrangement of items in a linear order of an already ordered set.

The symbol $P_{r} ^{n}$ = $\frac{n!}{(n-r)!}$

is used to denote the number of permutations of n distinct objects, taken r at a time.

According to the question

Website requires users to create a password consisting of digits only.

i.e  Digits are:

0 , 1 , 2 , 3 , 4 , 5 , 6 , 7 , 7 , 8 , 9 = total 10 digits

no digit may be repeated and each password must be at least 9 digits.

i.e Digits taken at a time is 9 with no repetitions

Now ,

Applying permutation

$P_{r} ^{n}$ = $\frac{n!}{(n-r)!}$

substituting the value

n = 10

r = 9

$P_{9} ^{10}$ = $\frac{10!}{(10-9)!}$

$P_{9} ^{10}$ = 10!

     = 3,628,800

Hence, There are 3,628,800 possible ways to create passwords .

To know more about  permutations here:

https://brainly.com/question/1216161

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