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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 isA. `89`B. `109`C. `78`D. `57` |
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Answer» 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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