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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

Monjur Alahi

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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Salim Ahmed Kawsar

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Correct Answer - B
`(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`

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