Respuesta :
This question is incomplete
Complete Question
Among the seven nominees for two vacancies on the city council are three men and four women. In how many ways may these vacancies be filled
a) with any two of the nominees?
b) with any two of the women?
c) with one of the men and one of the women?
Answer:
a) 21 ways
b) 6 ways
c) 12 ways
Step-by-step explanation:
We solve this question using combination formula
C(n, r) = nCr = n!/r! (n - r)!
a) with any two of the nominees?
Probability (two of the nominees) = 7C2
= 7!/2! ×(7 - 2)!
= 7!/ 2! × 5!
= 7 × 6 × 5 × 4 × 3 × 2 × 1/2 × 1 ×(5 × 4 × 3 × 2 × 1)
= 21
b) with any two of the women?
We have a total of 4 women
Hence, the probability of any two of the four women, filling the vacancies =
P(any two of the women) = 4C2
= 4!/2! ×( 4 - 2)!
= 4!/ 2! × 2!
= 4 × 3 × 2 × 1/ 2 × 1 ×( 2 × 1)
= 6
c) with one of the men and one of the
Total number of men = 3
Total number of women = 4
= 3C1 × 4C1
= [3!/1! ×(3 - 1)! ] × [4!/1! ×(4 - 1)! ]
= [3!/1! × 2!] × [4!/1! ×3!]
= [3 × 2 × 1/ 1 × 2 × 1] × [4 × 3 × 2 × 1/ 1 × 3 × 2 × 1]
= 3 × [24/6]
= 3 × 4
= 12 ways
The probability for any two of the nominees is 21
The probability for two women is 6
This question is incomplete
Complete Question
Among the seven nominees for two vacancies on the city council are three men and four women. In how many ways may these vacancies be filled
a) with any two of the nominees?
b) with any two of the women?
We have given,
Total number of nominees for two vacancy =7
We solve this question using combination formula
What is the formula for combination?
[tex]C(n, r) = nCr = n!/r! (n - r)![/tex]
a) with any two of the nominees?
Total number of nominees(n)=7
We are selecting r nominees r=2
Probability = 7C2
= [tex]\frac{7!}{2! (7 - 2)!}[/tex]
= 7!/ 2! × 5!
= 21
b) with any two of the women?
We have a total number of women=4
Out of 4 we have select 2 women
Hence, the probability of any two of the four women is
4C2
= 4!/2! ×( 4 - 2)!
= 4!/ 2! × 2!
= 6
Therefore,probability for two women is 6
To learn more about the combination visit:
https://brainly.com/question/25821700
