Question 1085166
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Let
A = number of ways to choose 2 females
B = number of ways to choose 2 people (any gender)


Order will not matter. 


There are 3 ways to pick 2 females. Let's consider the group of females {X,Y,Z} where the letters are codenames for their actual names
The three groups we can form are: {X,Y}, {Y,Z}, {X,Z}
Each group in a set of curly braces
Note how order does not matter. Something like {X,Y} is the same as {Y,X}


An alternative viewpoint is to consider that there are 3 ways to not pick a female. The three cases would be {X}, {Y}, and {Z}


If you wish to use a formula, then you can use the nCr combination formula to get
n C r = (n!)/(r!*(n-r)!)
3 C 2 = (3!)/(2!*(3-2)!)
3 C 2 = (3!)/(2!*1!)
3 C 2 = (3*2!)/(2!*1!)
3 C 2 = (3)/(1!)
3 C 2 = (3)/(1)
3 C 2 = 3/1
3 C 2 = 3
So that confirms the previous results
In this case, n = 3 because there are three applicants to choose from and r = 2 because that's the number of selections made


So far, we know that A = 3 because there are three ways to pick two women (from a pool of 3).

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Using the same formula, but now with n = 10 (there are 10 people total), we get
n C r = (n!)/(r!*(n-r)!)
10 C 2 = (10!)/(2!*(10-2)!)
10 C 2 = (10!)/(2!*8!)
10 C 2 = (10*9*8!)/(2!*8!)
10 C 2 = (10*9)/(2!)
10 C 2 = (10*9)/(2*1)
10 C 2 = 90/2
10 C 2 = 45


Indicating that there are 45 different unique groups we can form if we do not worry about the gender of who is selected.


This means that B = 45

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Now divide the values A and B to get A/B = 3/45 = 1/15


The probability as a fraction is 1/15. Don't forget to fully reduce. This value is exact.


Because your teacher wants the answer in decimal form, you would use a calculator or long division to get 1/15 = 0.06666666666667 which is approximate. That value rounds to 0.067


Because this answer isn't listed, I'm assuming there's a typo somewhere. A guess I have is that choice D should be 0.067 instead of 0.67


Or perhaps choice D should be 0.07 instead of 0.67


In any event, I'm thinking your teacher meant to have the answer be choice D. I would check with the teacher though.


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Final Answer: <font color="red">choice D) 0.67</font>
Note: Look at the section above for an explanation


Edit: MathLover1's solution makes sense on the surface, but looking at it closer there's a flaw in the logic. The answer (3/10)*(3/10) = 9/100 = 0.09 would only apply if the first applicant chosen is put back into the pool. It doesn't make sense to select the same applicant twice.
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