A delegation of five students is to be formed from a group of 10 students. If three particular students want to
remain together whereas two particular students do not want to remain together then the number ofselections, is

A.B. C want to remain together.

D,E do not want to remain together.

 In                            Out                  Number  of Selections

A, B, C, D                E                     ${ }^5{C}_1=5$

A,B,C.E                   D                     ${ }^5{C}_1=5$

D                            A,B,C,E              ${ }^5{C}_4=5$

E                            A,B,C,D               ${ }^5{\mathrm{C}}_4=5$

Required number of selections is

${ }^5{\mathrm{C}}_1{+}^5{\mathrm{C}}_1{+}^5{\mathrm{C}}_4{+}^5{\mathrm{C}}_4=20$