Question 1039942
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Part A) In how many ways can three people be selected from this group of fifteen?


There are 15 people total. We want to select 3 of them.


n = 15
r = 3


Use the <a href="http://www.mathwords.com/c/combination_formula.htm">combination formula</a> to get


n C r = (n!)/(r!(n-r)!)


15 C 3 = (15!)/(3!*(15-3)!)


15 C 3 = (15!)/(3!*12!)


15 C 3 = (15*14*13*12!)/(3!*12!)


15 C 3 = (15*14*13)/(3!)


15 C 3 = (15*14*13)/(3*2*1)


15 C 3 = (2730)/(6)


15 C 3 = 455


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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: <font color=red>455</font>
Answer to part B: <font color=red>56</font>
Answer to part C: <font color=red>0.12307692307692</font>


The result for part C is approximate. 
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