Number of natural number upto one lakh, which contains $1, 2, 3,$ exactly once and remaining digits any time is--

2940

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2850

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2775

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2680

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Solution

The correct option is A $2940$
$100000$

3 digit 1 2 3 =3 ! =6

4 digit 1 2 3 = $6 c_{1} .4!$

(without 0) $= 144$

(with 0) 1 2 3 $= 3 c_{1} \times 3!$

$= 1 θ$

5 digit................ $5 c_{3} .3! \times 36$

(without 0) $= 2160$

(with 10) ................. $4 c_{1} .4! \times 6$ $= 576$

(with 20) 1......2..3 $4 c_{2} .3!$ $= 36$
$= 2940$

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Number of natural number upto one lakh, which contains 1,2,3, exactly once and remaining digits any time is--

The correct option is A 2940100000 3 digit 1 2 3 =3 ! =6 4 digit 1 2 3 =6c1.4! (without 0) =144 (with 0) 1 2 3 =3c1×3! =1θ 5 digit................ 5c3.3!×36 (without 0) =2160 (with 10) ................. 4c1.4!×6 =576 (with 20) 1......2..3 4c2.3! =36=2940

Number of natural number upto one lakh, which contains $1, 2, 3,$ exactly once and remaining digits any time is--