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.

Name: 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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Description: 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.

#NCERT
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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 in each arrangement P₁ must occur whereas P₄ and P₅ do not occur. Find the number of such possible arrangements. [Hint: Required number of arrangement $=7C_4\times 5!$ ]

Answers (1)

Given that $P_1,P_2,P_3, ... P_{10}$

persons out of which 5 are to be arranged but $P_1$ must occur

whereas P₄and P₅ never occur. So, now we only have to select 4 out of 7 persons

Number of selections= $^7C_4=35$

Number of the arrangement of 5 persons= $35*5!=35*120=4200$

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There are 10 persons named . 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. [Hint: Required number of arrangement ]

Answers (1)

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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 in each arrangement P₁ must occur whereas P₄ and P₅ do not occur. Find the number of such possible arrangements. [Hint: Required number of arrangement $=7C_4\times 5!$ ]