Question

How many numbers greater than 1000000 can be formed by using the digits 1, 2, 0, 2, 4, 2, 4 ?

Answer 1

Total number of digits = 7

Now,

Number of 7-digit numbers = $\frac{7!}{3!2!}$

=$\frac{7\times 6\times 5\times 4\times 3}{3!\times 2}$

=$7\times 6\times 5\times 2$

= 420

And, 0 cannot be first digit of the 7-digit numbers

$\therefore$ Number of 6-digit numbers

= $\frac{6!}{3!2!}$

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

= $6\times 5\times 2$

= 60

Hence, total number of 7-digit number which are greater than 1000000= 420-60=360