Question

How many numbers greater than a million can be formed with the digits $2,3,0,3,4,2,3$?

Answer 1

One million has $7$ digits i.e. $6$ zeros

So, numbers greater than a million will have atleast $7$ digits

$-------$

$1st$ place can't be zero
$1st$ place $-2-$ Numbers left $(3,0,3,4,2,3)$
No. of ways of arranging remaining digits $=\frac{6!}{3!}=120$
$1st$ place $-3-$ Numbers left $(2,3,0,3,4,2)$
No. of ways of arranging remaining digits $=\frac{6!}{2!2!}=180$
$1st$ place $-4-$ Numbers left $(2,3,0,3,2,3)$
No. of ways of arranging remaining digits $=\frac{6!}{3!2!}=60$
Then, total no. of ways $=120+180+60=360.$