Question

The number of 4 digit number that can be formed from the digits 0, 1, 2, 3, 4, 5, 6, 7 so that each number contains digit 1 is

Answer 1

The number of $4$ digits number that can be form from the digits

$0,1,2,3,4,5,6,7$ so that the each number contains digit $1$ is

Given that number is of 4 digits so the first digit can't be $0$.

Let (i) first digit is $\left(1\right)$.

(ii) first digit is not $1$

(i) First digit is $1$

We pick $3$ digits in order out of the remaining $\mathrm{7.6.5}=210$ possibilities.

(ii) First digit is not $1$

There are $6$ ways to choose the first digit $(2,3,4,5,6,7)$,

$3$ ways to place the digit $1$ (hundreds, tens, ones)

and $6.5$ ways to choose the other digits

So $\mathrm{6.3.6.5}=540$ possibilities

$\therefore$ total possibilities are $210+540=750$

$750$ possibilities to choose the number that to each number contains digit $1$