10 equally qualified applicants; six men and four women apply for three lab technician positions. Unable to justify choosing any of the applicants over all the others, the personnel director decides to select the three at random. Let X denote the number of men hired. Compute the standard deviation of X
probability of selecting no man = p(0) = 6C0 * 4C3/10C3
here, nCr = n!/(r!*(n-r)!)
=> p(0) = 1*4*(1*2*3)/(10*9*8) = 0.033
p(1) = 6C1*4C2/10C3 = ...
The random variables and the variances are computed. The applicants of three lab technician positions are examined. The solution answers the question(s) below.