Mar 21, 2025 at 12.00 am
In the textbook, Section 5.5 Counting Techniques discusses permutations and combinations.

Once certain conditions are met, the number of arrangements of objects from distinct objects, where repetition is not allowed, can be determined using combinations or permutations. Which condition needs to
be determined before deciding to use combinations or permutations to calculate the number of arrangements of objects from distinct objects, where repetition is not allowed?

When using combinations or permutations, is it possible that ? Why or why not?

Ask by Lowe Norton. in the United States

Mar 26,2025

Question

Mar 21, 2025 at 12.00 am
In the textbook, Section 5.5 Counting Techniques discusses permutations and combinations.

Once certain conditions are met, the number of arrangements of objects from distinct objects, where repetition is not allowed, can be determined using combinations or permutations. Which condition needs to
be determined before deciding to use combinations or permutations to calculate the number of arrangements of objects from distinct objects, where repetition is not allowed?

When using combinations or permutations, is it possible that ? Why or why not?

Ask by Lowe Norton. in the United States

Mar 26,2025

UpStudy AI · Accepted Answer

1) The key condition is whether the order of the $$ r $$ objects matters.  
- If order matters, the problem deals with permutations.  
- If order does not matter, the problem deals with combinations.

2) No, it is not possible for $$ r > n $$ when repetition is not allowed.  
- Since the $$ n $$ objects are distinct and repetition cannot be used to "replace" an object already chosen, it is impossible to select more than $$ n $$ objects.  
- If $$ r > n $$, there aren’t enough distinct objects to form the arrangement.
1) Determine if the order of the $$ r $$ objects matters. - If order matters, use permutations. - If order does not matter, use combinations. 2) No, $$ r $$ cannot be greater than $$ n $$ when repetition is not allowed because there aren't enough distinct objects to form such an arrangement.

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