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A popular website requires users to create a password consis

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Senior Manager
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A popular website requires users to create a password consis [#permalink] New post 05 Oct 2017, 20:36
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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?

A. 9! + 10!
B. 2 x 10!
C. 9! x 10!
D. 19!
E. 20!

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Re: A popular website requires users to create a password consis [#permalink] New post 05 Oct 2017, 21:50
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Bunuel wrote:
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?

A. 9! + 10!
B. 2 x 10!
C. 9! x 10!
D. 19!
E. 20!

Kudos for correct solution.


Here there are two possibilities - (since it has asked for atleast 9 digit)

1. At least 9 digit

2. all 10 digit

in first case

Choosing 9 digit without repetition = 10 * 9 * 8 * 7 * 6 * 5 * 4 * 3 * 2 = 10! (since any number multiply by 1 is the number itself)

Choosing 10 digit without repetition = 10 * 9 * 8 * 7 * 6 * 5 * 4 * 3 * 2 * 1 = 10!

Therefore total no. ways = 2 * 10!
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Re: A popular website requires users to create a password consis   [#permalink] 05 Oct 2017, 21:50
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A popular website requires users to create a password consis

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