Question

Find the number of numbers, greater than a million, that can be formed with the digits 2,3,0,3,4,2,3.

Answer 1

Total number of digits = 7

Since, 0 cannot be first digit of the 7 digit numbers.

$\therefore$ Number of 6 -digit

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

[$\because$ 2 comes 2 times and 3 comes 3 times]

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

= $6\times 5\times 2$

= 60.
Now, number of 7-digit numbers = $\frac{7!}{2!3!}$

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

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

= 420
Hence, total number of numbers which is greater then 1 million = 420-60= 360.