Answer:
[tex]Probability = \frac{1}{969}[/tex]
Step-by-step explanation:
Given
[tex]Members = 19[/tex]
[tex]Selection = 3[/tex]
Required
Determine the probability of selecting Jim, Bruce and Valerie
First, we need to calculate the possible number of selections.
This is calculated using combination formula:
[tex]Selection = ^nC_r[/tex]
[tex]Selection = ^{19}C_3[/tex]
[tex]Selection = \frac{19!}{(19-3)!3!}[/tex]
[tex]Selection = \frac{19!}{16!3!}[/tex]
[tex]Selection = \frac{19 * 18 * 17 * 16!}{16! * 3 * 2 * 1}[/tex]
[tex]Selection = \frac{19 * 18 * 17}{3 * 2 * 1}[/tex]
[tex]Selection = \frac{19 * 18 * 17}{6}[/tex]
[tex]Selection = 969[/tex]
Selection of Jim, Bruce and Valerie is only 1 selection of the 960 possible selection.
So:
[tex]Probability = \frac{1}{969}[/tex]
The probability that Jim, Bruce, and Valerie are selected in any order is [tex]\rm P=\dfrac{1}{969}[/tex] and this can be determined by using the given data.
Given :
Assume that Jim, Bruce, and Valerie are three of the 19 members of the class and that three of the class members will be chosen randomly to deliver their reports during the next class meeting.
In order to determine the probability that Jim, Bruce, and Valerie are selected in any order, first determine the total number of possible selections.
The total number of possible selections is given by:
[tex]\rm S = \; ^nC_r[/tex]
[tex]\rm S = \; ^{19}C_3[/tex]
[tex]\rm S = \dfrac{19!}{16! \times 3!}[/tex]
S = 969
So, the probability that Jim, Bruce, and Valerie are selected in any order is:
[tex]\rm P=\dfrac{1}{969}[/tex]
For more information, refer to the link given below:
https://brainly.com/question/21586810
