Question:
How many 7 - digit numbers can be formed by using the digits 1, 2, 0, 2, 4, 2, 4?
Solution:
To find: number of 7 digit
0 cannot be in the first place because that would make a 6 digit number
Total number of 7 - digit numbers = Total number of number possible - Number of numbers with 0 at the first place
Total number of numbers possible $=\frac{7 !}{3 ! 2 !}=420$
Number of numbers with 0 at first place $=\frac{6 !}{3 ! 2 !}=60$
$\Rightarrow$ Number of 7 - digit numbers $=420-60=360$
360 seven - digit numbers are possible