Ellie wants to change her password which is ELLIE9 but with same letters and number. In how
many ways she can do that?
P = 256
P = 150
P = 200
P = 179

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konrad509 konrad509 · Answer 1 · 2019-07-12T09:58:34+02:00

[tex]\dfrac{6!}{2!2!}-1=\dfrac{3\cdot4\cdot5\cdot6}{2}-1=180-1=179[/tex]

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MrRoyal MrRoyal · Answer 2 · 2021-12-09T12:21:07+01:00

The number of passwords she can create is an illustration of permutations.

The number of ways to create the password is 179

The password is given as: ELLIE9

The number of characters in the password is:

[tex]n = 6[/tex]

L and E are repeated twice.

So, we have

[tex]L = 2[/tex]

[tex]E = 2[/tex]

The number of new passwords to create is then calculated as:

[tex]Passwords = \frac{n!}{L!E!} - 1[/tex] --- 1 represents the current password

This gives

[tex]Passwords = \frac{6!}{2!2!} - 1[/tex]

Expand

[tex]Passwords = \frac{6 \times 5 \times 4 \times 3 \times 2!}{2! \times 2 \times 1} - 1[/tex]

[tex]Passwords = \frac{6 \times 5 \times 4 \times 3 }{2 \times 1} - 1[/tex]

Simplify

[tex]Passwords = 180 - 1[/tex]

Subtract

[tex]Passwords = 179[/tex]

Hence, the number of ways to create the password is 179