How many 6 – digit numbers can be formed by using the digits 4, 5, 0, 3, 4, 5?
Question:

How many 6 – digit numbers can be formed by using the digits 4, 5, 0, 3, 4, 5?

 

Solution:

To find: number of 6 digit

0 cannot be in the first place because that would make a 5 – digit number

Total number of 6 – digit numbers = Total number of number possible – Number of numbers with 0 at the first place

Total number of numbers possible $=\frac{6 !}{2 ! 2 !}=180$

Number of numbers with 0 at first place $=\frac{5 !}{2 ! 2 !}=30$

$\Rightarrow$ Number of 6 – digit numbers $=180-30=150$

150 six – digit numbers are possible

 

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