[tex] \displaystyle
|\Omega|=\binom{14}{4}=\dfrac{14!}{4!10!}=\dfrac{11\cdot12\cdot13\cdot14}{2\cdot3\cdot4}=1001\\
|A|=\binom{8}{4}=\dfrac{8!}{4!4!}=\dfrac{5\cdot6\cdot7\cdot8}{2\cdot3\cdot4}=70\\\\
P(A)=\dfrac{70}{1001}=\dfrac{10}{143}\approx7\% [/tex]
Answer:
The probability that the committee consists of all boys is:
[tex]\dfrac{10}{143}[/tex]
Step-by-step explanation:
Since a committee of four people is to be formed from a group of:
8 boys and 6 girls.
This implies total number of people= 14.
Probability that the committee consist of all boys is calculated by taking the ratio of probability of selecting 4 boys from all boys and selecting 4 person from total number of person.
Hence, the probability is calculated by:
[tex]\text{Probability}=\dfrac{8_C_4}{14_C_4}[/tex]
Now,
[tex]8_C_4=\dfrac{8!}{4!\times (8-4)!}\\\\\\8_C_4=\dfrac{8!}{4!\times 4!}[/tex]
and
[tex]{14}_C_4=\dfrac{14!}{4!\times (14-4)!}\\\\\\14_C_4=\dfrac{14!}{4!\times 10!}[/tex]
Hence, the probability is given by:
[tex]\text{Probability}=\dfrac{10}{143}[/tex]
Hence, the probability is:
[tex]\dfrac{10}{143}[/tex]
