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There are 10 persons named P1, P2, P3, ... 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 number of such possible arrangements.

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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

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