Respuesta :
An experimenter is randomly sampling 4 objects in order from among 41 objects. What is the total number of samples in the sample space?
Answer: There are 41 objects in total.
An experimenter needs to randomly select 4 objects in order among 41 objects.
Please note an experimenter needs to select random sample in order. Therefore, we need to use Permutation formula to find the total possible samples in the sample space.
[tex]41P4=\frac{41!}{(41-4)!}[/tex]
[tex]=\frac{41}{37!}[/tex]
[tex]=2430480[/tex]
Therefore, the total number of samples in the sample space is [tex]2430480[/tex]
The total sample is 2,430,480.
Permutation and combination
A permutation is an act of arranging the objects or elements in order. Combinations are the way of selecting objects or elements from a group of objects or collections, in such a way the order of the objects does not matter.
Given
An experimenter is randomly sampling 4 objects in order from among 41 objects.
To find
The total number of samples in the sample space.
How to find the total number of samples in the sample space?
An experimenter is randomly sampling 4 objects in order from among 41 objects. then the total sample will be,
[tex]\rm Total\ sample =\ \ ^{41}P_4\\\\\rm Total\ sample = \dfrac{41!}{(41 - 4)!}\\\\\rm Total\ sample = \dfrac{41 * 40*39*38*37!}{37!}\\\\\rm Total\ sample = 41*40*39*38\\\\\rm Total\ sample = 2430480[/tex]
Thus, the total sample is 2,430,480.
More about the permutation and combination link is given below.
https://brainly.com/question/11732255
