there are 10 persons named p1,p2,................,p10.out of 10 persons ,5 persons are to be arranged in a line such that in each arrangement p1 must occur whereas p4 and p5 do not occur. find the no of such possible arrangements.

Given that, P1 , P2 , …, P10 , are 10 persons, out of which 5 persons are to be arranged but P, must occur whereas P4 and P5 never occurs. As P, is already occurring w’e have to select now 4 out of 7 persons. .'. Number of selections = 7C4 = 35 Number of arrangements of 5 persons = 35 x 5! = 35 x 120 = 4200