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Permutations - the meaning of "distinct" and "no repetitions" [Solved!]

My question

Good Evening!

Taking cue from your example of arranging 4 resistors, we have 4! ways of arranging the resistors in series

1. if we assume that each resistor has a different resistance, does that mean they are distinct?

2. when will they NOT be distinct? will it if for example R1=R2= 5 ohms?

3. The meaning of repetitions. i did the tree diagram of the entire set of the 4 resistors and there were no repetitions. can pls explain what wd be regarded as a repetition?

thank u

this refers to Theorem 2 in the link below

3. Permutations

What I've done so far

4 x 3 x 2 x 1

X

Good Evening!

Taking cue from your example of arranging 4 resistors, we have 4! ways of arranging the resistors in series

1. if we assume that each resistor has a different resistance, does that mean they are distinct?

2. when will they NOT be distinct? will it if for example R1=R2= 5 ohms?

3. The meaning of repetitions. i did the tree diagram of the entire set of the 4 resistors and there were no repetitions. can pls explain what wd be regarded as a repetition?

thank u

this refers to Theorem 2 in the link below
Relevant page

<a href="/counting-probability/3-permutations.php">3. Permutations</a>

What I've done so far

4 x 3 x 2 x 1

Re: Permutations - the meaning of "distinct" and "no repetitions"

Hello Mansoor

1. Yes, a "distinct" resistor in this case would mean each one has a different resistance.

2. If two of them had the same resistance as you suggest, then we would have 3 distinct "groups". You would then need to use Theorem 3 from that page.

3. In Example 5 on that page, there are 2 m's and 2 a's. The m's are a case of repetitions, as are the a's.

But I suspect your question is more closely related to the Combinations section, where order is not important and repetitions can occur.

Hope it helps.

X

Hello Mansoor

1. Yes, a "distinct" resistor in this case would mean each one has a different resistance.

2. If two of them had the same resistance as you suggest, then we would have <b>3</b> distinct "groups". You would then need to use Theorem 3 from that page.

3. In Example 5 on that page, there are 2 m's and 2 a's. The m's are a case of repetitions, as are the a's.

But I suspect your question is more closely related to the <a href="/counting-probability/4-combinations.php">Combinations</a> section, where order is not important and repetitions can occur.

Hope it helps.

Re: Permutations - the meaning of "distinct" and "no repetitions"

ur last para may just summarize my confusion.in that, i may not be able to tell when to use permutations and when to use combinations. But i suspect that if i keep at it, i will get it one of these days.

I have a particular problem that i want to ask about - permutatons again...and is it ok to ask here or shd i create a new post?

regards

X

Thank u for the reply.

ur last para may just summarize my confusion.in that, i may not be able to tell when to use permutations and when to use combinations. But i suspect that if i keep at it, i will get it one of these days.

I have a particular problem that i want to ask about - permutatons again...and is it ok to ask here or shd i create a new post?

regards

Re: Permutations - the meaning of

X

@Mansoor: If it's a new question, please start a new thread.

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