Respuesta :
A person eating at a cafeteria must choose 4 of the 13 vegetables on offer. calculate the number of elements in the sample space for this experiment.
Answer: The number of elements in the sample space for this experiment can be found using the combination formula because the order does not matter here.
Therefore, the number of elements in the sample space for this experiment is:
[tex]13C4=\frac{13!}{(13-4)!4!}[/tex]
[tex]=\frac{13!}{9! \times 4!}[/tex]
[tex]=\frac{6227020800}{8709120}[/tex]
[tex]=715[/tex]
Therefore, the number of elements in the sample space for this experiment is 715.
Using its concept and the combination formula, it is found that there are 715 elements in the sample space for this experiment.
What is the sample space of an experiment?
The sample space is the set that contains all possible outcomes for an experiment.
In this problem, the order in which the vegetables are chosen is not important, hence the combination formula is used to solve this question.
What is the combination formula?
[tex]\rm ^nC_x[/tex] is the number of different combinations of x objects from a set of n elements, given by:
[tex]\rm ^nC_x = \dfrac{n!}{(n-x)!x!}[/tex]
We have that 3 vegetables are taken from a set of 14, hence:
[tex]\rm ^nC_x = \dfrac{n!}{(n-x)!x!}\\\\\rm ^{13}C_4 = \dfrac{13!}{(13-4)!4!}\\\\ ^{13}C_4 = \dfrac{13!}{9!4!}\\\\ ^{13}C_4 = 715[/tex]
Hence, there are 715 elements in the sample space for this experiment.
You can learn more about sample space at; https://brainly.com/question/25861936
