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The keypad to the lock to the computer lab has 5 buttons. An access code is a sequence of 3 buttons or 4 buttons. Find the number of access codes: (a) If a button may be repeated. (b) If a button may not be repeated.

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Answer:

(a) 750 codes

(b) 180 codes

Step-by-step explanation:

The number of possible access codes is given by the number of ways to pick 3 out of 5 buttons added to the number of ways to pick 4 out of 5 buttons, in which the order matters.

(a) If a button may be repeated.:

[tex]n=5*5*5*5+5*5*5\\n=750\ codes[/tex]

There are 750 possible codes.

(b) If a button may not be repeated.

[tex]n=5*4*3*2+5*4*3\\n=180\ codes[/tex]

There are 180 possible codes.

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