Question

There are 10 persons named `P_1, P_2, P_3 ..., P_10`. Out of 10 persons, 5 persons are to be arranged in a line such that is each arrangement `P_1` must occur whereas `P_4` and `P_5` do not occur. Find the number of such possible arrangements.

Answer 1

Given that `P_(1), P_(2),…,P_(10)`, are 10 persons, out of which 5 persons are to be arranged but `P_(1)` must occur whereas `P_(4) " and " P_(5)` never occur.
`therefore` Selection depends on only 10 - 3 = 7 persons
As, we have already occur `P_(1)`, Therefore, we have to select only 4 persons out of 7.
Number of selection `= ""^(7)C_(4) = (7"!")/(4"!"(7-4)"!") = (7"!")/(4"!" 3"!") = (5040)/(24 xx 6) = 35`
`therefore` Required number of arrangement of 5 persons `= 35 xx 5"!" = 35 xx 120 = 4200`