The number of arrangements of all digits of 12345 such that at least 3 digits will not come in its position is

Step-by-step solution

Total number of ways such that at least 3 digits will not come in its position = ^5 C₃ 3!- ^3 C₁ 2!+ ^3 C₂ 1!- ^3 C₃ 0! + ^5 C₄ 4!- ^4 C₁(3!)+ ^4 C₂(2!)- ^4 C₃(1!)+ ^4 C₄ .(0!) + ^5 C₄ 5!- ^5 C₁ 4!+ ^5 C₇ 3!- ^5 C₂ 2!+ ^5 C₄ 1!- . . ^5 C₅(0!) =10(2)+5(9)+(44)=20+45+44=109