Solution

 a. Experiment is assigning four men to four one-man jobs, among them two are from minority group.

b. Let $M_1$ and $M_2$ be men from minority and $N_1$ and $N_2$ be men from non-minority group.

Let $J_1, J_2, J_3, J_4$ represent the jobs, ordered in decreasing order of desirability.

Let $xyz$ represent the event that man $x, y$ and $z$ is assigned to job $J_1, J_2$ and $J_3.$

S=⎩⎨⎧​M1​M2​N1​,M1​M2​N2​,M1​N1​N2​,M2​N1​N2​,​M1​N1​M2​,M1​N2​M2​,M1​N2​N1​,M2​N2​N1​,​M2​M1​N1​,M2​M1​N2​,N1​M1​N2​,N1​M2​N2​,​M2​N1​M1​,M2​N2​M1​,N1​N2​M1​,N1​N2​M2​,​N1​M1​M2​,N2​M1​M2​,N2​M1​N1​,N2​M2​N1​,​N1​M2​M1​N2​M2​M1​N2​N1​M1​N2​N1​M2​​⎭⎬⎫​

$$S= \left\{ \begin{matrix} M_1M_2N_1, & M_1N_1M_2, & M_2 M_1 N_1, & M_2 N_1 M_1,& N_1M_1 M_2 , &N_1M_2 M_1\\ M_1M_2N_2, & M_1N_2M_2, & M_2 M_1 N_2, & M_2 N_2 M_1,& N_2M_1 M_2 , &N_2M_2 M_1\\ M_1N_1N_2, & M_1N_2N_1, & N_1 M_1 N_2, &N_1 N_2 M_1,& N_2M_1 N_1 , &N_2N_1 M_1\\ M_2N_1N_2, & M_2N_2N_1, & N_1 M_2 N_2, &N_1 N_2 M_2,& N_2M_2 N_1 , &N_2N_1 M_2\\ \end{matrix} \right\}$$

c. The two minority men are assigned the least desirable jobs are when first two jobs are given to $$N_1N1​ and $$N_2N2​. The number of such simple events is 4.

P(Two men from minority group get least desirable jobs =

 No. of favorable Simple

Total no. of Simple event

=4/24

=1/6

Answer

c. $$\dfrac{1}{6}