Question 1190190
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n = number of total staff members
r = number of staff members selected to go to the undisclosed secure location


We're told that r = 5, but we don't know what n is.
The list of possible options are: 7, 8, 9, 10, 11
which are drawn from choices A through E.


If n = 7, then,
C(n,r) = (n!)/(r!(n-r)!) .............. nCr combination formula
C(7,5) = (7!)/(5!*(7-5)!)
C(7,5) = (7!)/(5!*2!)
C(7,5) = (7*6*5*4*3*2*1)/((5*4*3*2*1)*(2*1))
C(7,5) = (5040)/((120)*(2))
C(7,5) = (5040)/(240)
C(7,5) = 21


I used the nCr combination formula because order doesn't matter. 


We see that n = 7 and r = 5 makes 21 different groups, which fits the criteria of "at least 20" (aka "20 or more").


Using larger values of n will make C(n,r) larger than 21.
You can use Pascal's Triangle as an alternative route to computing the nCr values.


Answer: A) 7
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