thats a very lengthy method the one which i've given is the shortest

 

i'll explain it a bit more clearly

 

 since there is no condition on the persons not selected therefore let us place them first

Let the persons not selected be A,B,C,D,E,F

 

  _A_B_C_D_E_F_

therefore the persons which are selected(4) have 7 places for themselves to select therefore no. of ways of selecting 4 places out of 7 are ⁷C₄= 35 ways