Among the seven nominees for two vacancies on a city council are three men and four women. In how many ways can these vacancies be filled

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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?

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

step-by-step explanation:

idk the answer i want to say 10 but then it would be equal so try 9 but then yeah so yeah we love edgen

this excerpt is taken from the book “we shall not be moved : the women’s factory strike of 1909 “ and is written by joan dash. it is the story of the great strike when almost 30thousand women working in factories in america formed a union to fight unsafe working conditions, long working hours and miserable wages.

question: which best states the author’s purpose for including this information in the text?

answer: to challenge the reader’s ideas about a historical event