A team of four students is to be selected from a total of 12 students. The total number of ways in which the. team can be selected such that two particular students refuse to be together and other two particular students wish to be together only is equal to

Let S₁ and S₂ refuse to be together and S₃ and S₄ want to be together only. The total number of ways when S₃ and S₄ are selected is$\left({ }^8{\mathrm{C}}_2{+}^2{\mathrm{C}}_1{\times }^8{\mathrm{C}}_1\right)=44$. The total ways when S₃ and S₄ are not selected is $\left({ }^8{\mathrm{C}}_4{+}^2{\mathrm{C}}_1{\times }^8{\mathrm{C}}_3\right)=182$. Thus, the total number of ways is 44 + 182 = 226.