SOLUTION: A group consists of seven men and eight women. Three people are selected to attend a conference.
a. In how many ways can three people be selected from this group of fifteen?
b. I
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-> SOLUTION: A group consists of seven men and eight women. Three people are selected to attend a conference.
a. In how many ways can three people be selected from this group of fifteen?
b. I
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Question 1039942: A group consists of seven men and eight women. Three people are selected to attend a conference.
a. In how many ways can three people be selected from this group of fifteen?
b. In how many ways can three women be selected from the eight women?
c. Find the probability that the selected group will consist of all women. Answer by jim_thompson5910(35256) (Show Source):
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Part B) In how many ways can three women be selected from the eight women?
There are 8 women and we want to choose 3 of them.
Similar to part A, we use the combination formula with n = 8 and r = 3
n C r = (n!)/(r!(n-r)!)
8 C 3 = (8!)/(3!*(8-3)!)
8 C 3 = (8!)/(3!*5!)
8 C 3 = (8*7*6*5!)/(3!*5!)
8 C 3 = (8*7*6)/(3!)
8 C 3 = (8*7*6)/(3*2*1)
8 C 3 = (336)/(6)
8 C 3 = 56
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Part C) Find the probability that the selected group will consist of all women.
Divide the two values from parts A and B to get...
(result from part B)/(result from part A) = (# of ways to pick 3 women)/(# of ways to pick 3 people)
(result from part B)/(result from part A) = 56/455
(result from part B)/(result from part A) = 0.12307692307692
This is approximate.
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Summary:
Answer to part A: 455
Answer to part B: 56
Answer to part C: 0.12307692307692
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