SOLUTION: 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 no

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Question 934133: 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.

Answer by Theo(13342) (Show Source):
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10 persons are in the line.
you want to arrange 5 out of the 10 but you don't want p4 and p5.
this leaves 8 that you want to arrange in groups of 5.
that's the permutation formula of 8p5 = 8! / (8-5)! = 8! / 3! = 6720

now you want to make sure p1 is in all of the groups.

to determine how many groups require p1 to be in them, determine how many groups can be made without p1 in them.

that would be the permutation formula of 7p5 = 2520.

the number of groups that must have p1 in them are therefore the number of groups that could have p1 in them minus the number of groups that don't have p1 in them which is equal to 6720 - 2520 = 4200.