Permutations and Combinations 1995 3U HSC (1 Viewer)

[Raeksis]

Question 3a of the 1995 3u paper says:

A security lock has 8 buttons labelled as shown. Each person using the lock is given a 3 letter code.
i. How many different codes are possible if letters can be repeated and their order is important.

The answer in the SuccessOne book just says 8³.

In the Phoenix Questions by Topic book (the edition after they lost publishing rights to HSC questions) the question is there but slightly ammended:

A security combination lock has 8 touchpads as shown. Each person cleared to use the safe containing the lock is allocated a 3-digit code.
i. How many different codes are possible if the order is unimportant and the digits can be repeated?

Interestingly, the answers also have 8³... That isn't right since the order is unimportant I think

One of these is wrong and I'm thinking it's Pheonix although Perms and Comms is my weakest topic... Could anyone shed some light on this?

 

[braintic]

The actual question had 3 parts:

A security lock has 8 buttons labelled as shown. Each person using the lock is given a 3-letter code.
(i) How many different codes are possible if letters can be repeated and their order is important?
(ii) How many different codes are possible if letters cannot be repeated and their order is important?
(iii) Now suppose that the lock operates by holding 3 buttons down together, so that order is NOT important. How many different codes are possible?

Their answers:
(i) 8^3 =512
(ii) 8P3 = 336
(iii) 8C3 = 56

 

[faisalabdul16]

Got the same answers as braintic, answers from textbook are correct

 

[Raeksis]

What would be the correct answer for the question in the Phoenix book where order is unimportant then? I'm thinking divide by 3!...

 

[photastic]

Braintic's answers are correct. I can add that another way to approach the 2nd part is a combination type, where 8C1x7C1x6C1 which is a logic type method.

 

[Raeksis]

Yes but I'm talking about part i with the order being unimportant as opposed to important as per Braintic's answer

 

[braintic]

Yes but I'm talking about part i with the order being unimportant as opposed to important as per Braintic's answer

8 + 8P2 + 8C3 =120

(The P and C is deliberate - not an error)

It would be a pretty silly question to ask though.
You can't hold the buttons down together if repetition is allowed, so what real-life codes with numbers typed sequentially don't care about order?