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

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The number of arrangments of all digits of 12345 such that at least 3 digits will not come in its position is
A. 89
B. 109
C. 78
D. 57

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(b) Total number of ways such that at least 3 digits will not occur in its position.
=^(5)C_(3){3!-^(3)C_(1)2!+^(3)C_(2)1!-^(3)C_(2)0!}+^(5)C_(4)[4!-^(4)C_(1)(3!)+^(4)C_(2)(2!)-^(4)C_(3)(1!)+^(4)C_(4)(0!)}+^(5)C_(5){5!-^(5)C_(1)4!+^(5)C_(2)3!-^(5)C_(3)2!+^(5)C_(4)1!-^(5)C_(5)(0!)}
=10(2)+5(9)+(44)
=20+45+44=109