Question

How many numbers greater than 10,00,000 can be formed with the digits 0,1,2,1,2,2,3

Answer 1

Image 1

No. of numbers starting with $1$ are $\frac{6!}{3!}=6\times 5\times 4$

$=30\times 4$

$=120$

No. of numbers starting with $2$ are (Image 2)

$\frac{6!}{2!2!}=\frac{6\times 5\times 4\times 3}{2}=30\times 6=180$

No. of numbers starting with $3$ are (Image 3)

$\frac{6!}{2!3!}=\frac{6\times 5\times 4}{2}=6\times 5\times 2=60$

$\therefore$Total no. of numbers are $120+180+60$

$=300+60=360$