The correct answer is:
C) 70/1001
Explanation:
Choosing 4 boys from a total of 8 boys is a combination of 8 taken 4 at a time:
[tex] _8C_4=\frac{8!}{4!4!}=70 [/tex]
Since they are all boys, we are choosing 0 girls from 6:
[tex] _6C_0=\frac{6!}{0!6!}=1 [/tex]
Choosing 4 students from 6+8=14 total students is a combination of 14 people taken 4 at a time:
[tex] _{14}C_4=\frac{14!}{4!10!}=1001 [/tex]
This gives us a probability of 70(1)/1001 = 70/1001.
If students are chosen at random, the probability that the committee consists of all boys 70/1001.
Probability refers to a possibility that deals with the occurrence of random events. The probability of all the events occurring need to be 1.
P(E) = Number of favorable outcomes / total number of outcomes
Choosing 4 boys from a total of 8 boys is a combination of 4 taken at a time
[tex]^{8}C_4=8! / 4!4![/tex]
= 70
Since they are all boys, we are choosing 0 girls from 6
[tex]^{6}C_0=1[/tex]
Choosing 4 students from 14 total students is a combination of 4 taken at a time
[tex]^{14}C_4=14! / 10!4![/tex]
= 1001
The probability that the committee consists of all boys
= 70/1001.
Learn more about probability here;
https://brainly.com/question/11234923
