How many 7 – digit numbers can be formed by using the digits
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

 

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