Respuesta :
Answer:
The first part is of permutations.
We are selecting 3 elements from three different elements {1,2,3}
Points given:
We permit overlapped elements for the sequence. Here "overlapped elements" indicates that repetition is allowed.
So when repetition is allowed and order matters, we use permutations.
Formula to compute permutation is:
Lets say n is the three elements {1,2,3}
We have to select 3 elements so r = 3
Total number of selections using permutations = [tex]n^{r}[/tex] = n × n × n
= 3³ = 3 * 3 * 3
= 27
This means if we have 3 different elements then we have have 3 choices each time for making a sequence.
Hence If we make a sequence selecting three elements from three different elements {1, 2, 3} and we permit overlapped elements for the sequence, then the total number of sequences is 27.
Step-by-step explanation:
The second part indicates combinations.
This is because the statement of the question: If we do not take into account the order.
When the order does not matter, we use combinations.
So when the order does not matter and repetition is allowed we use the following formula:
Total number of selections using combinations = (r + n - 1)! / r! (n - 1)!
= (3 + 3 - 1) ! / 3! (3 - 1)!
= (3 + 2) ! / 3! (2!)
= 5! / 3! 2!
= 5*4*3*2*1 / (3*2*1 ) (2*1)
= 120 / 6 * 2
= 120 / 12
= 10
So these are the number of combinations of 3 elements taken 3 at a time with repetition.
The total number that will be selected in the permutations is 27.
How to calculate the permutations?
Based on the information given, the total number of permutations will be:
= n³
= 3 × 3 × 3
= 27
Also, the total number of selection using combination will be:
= (3 + 3 - 1)! / 3!(3 - 1)!
= 120 / (6 × 2)
= 120/12
= 10
Learn more about permutations on:
https://brainly.com/question/1216161
