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katiebotts18
26.02.2020 •
Social Studies
A committee consists of eight women and twelve men. Three committee members will be chosen as officers. What is the probability that all the officers are women?
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Ответ:
The probability that all the officers are women is![\frac{56}{1140}](/tpl/images/0525/8212/03f43.png)
Explanation:
Given a committee consisting of 8 women and 12 men, from which 3 committee members are to be chosen as officers from a committee.
The total number of committee members is 8 + 12 = 20 members
C(n,r) =
which represents the number of combinations of taking r objects out of n.
The probability that all the officers are women = C(8,3) / C(20,3)
=![\frac{8!}{3!(8-3)!} / \frac{20!}{3!(20-3)!}](/tpl/images/0525/8212/11012.png)
=![\frac{8!}{3!5!} /\frac{20!}{3!17!}](/tpl/images/0525/8212/1d1a6.png)
=![\frac{56}{1140}](/tpl/images/0525/8212/03f43.png)
Therefore the probability that all the officers are women is![\frac{56}{1140}](/tpl/images/0525/8212/03f43.png)
Ответ:
0.049 (approximately)
Explanation:
Solution:
Since there is 8 women and 12 men, from which 3 are chosen as officers.
Use C(n,r)=n! ÷ (r!(n-r)!) to represent number of combinations of taking r objects out of n.
Therefore;
Ways to choose 3 women out of 8 = C(8, 3)
Ways to choose from 20 members = C(20,3)
Probability of choosing 3 women out of 20
= C(8,3)÷ C(20,3)
Substituting our values for n=8 and r=3 we get
8! ÷ 3!(8-3)!
Substituting 8-3 with 5
8! / 3!×5!
Expanding factorial and cancelling out
8×7×6×5! ÷ 3!×5!
Multiple out
336÷6 = 56
Substituting our values for n=8 and k=3 we get
20! ÷ 3!(20-3)!
Substituting 20-3 with 17
20! ÷ 3!×17!
Expanding factorial and cancelling out
20x19x18x17! ÷ 3!×17!
Multiple out
6840÷6
= 1140
= 56/1140
= 3/17
=0.049 (approximately)
Ответ: