সমাবেশ বিষয়ক

Seven person P1,P2......,P7P_1,P_2......, P_7 initially seated at chairs C1,C2,.....C7C_1,C_2,.....C_7 respectively.They all left there chairs simultaneously for hand wash. Now in how many ways they can again take seats such that no one sits on his own seat and P1P_1, sits on C2C_2 and P2P_2 sits on C3C_3 ?

হানি নাটস

C1C5C6C7P5P4P7P6P7P4P5P6P6P4P7P54!(111!+12!13!+14!)So,ln=11×4+10=54 \begin{array}{llll}C_{1} & C_{5} & C_{6} & C_{7} \\ P_{5} & P_{4} & P_{7} & P_{6} \\ P_{7} & P_{4} & P_{5} & P_{6} \\ P_{6} & P_{4} & P_{7} & P_{5} \\ 4! & \left(1-\frac{1}{1!}\right. & +\frac{1}{2!} & \frac{1}{3!} \\ & & \left.+\frac{1}{4!}\right) \\ So, \ln = & 11 \times 4+10 \\ & =54\end{array}

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