Question

In the same way, try placing the digit 4 in thousands place and get six different 4-digit
numbers. Also make different 4-digit numbers by fixing 8 and 5 in the thousands place.

Answer 1

4567
4123
4789
4089
4012
4561
4536

5678
8123

Hope it helps u

Answer 2

The six different 4-digit numbers by fixing 4 in thousands place are 4 3 2 1, 4 3 1 2, 4 2 1 3, 4 2 3 1, 4 1 3 2, 4 1 2 3

The six different 4-digit numbers by fixing 5 in thousands place are 5 3 2 1, 5 3 1 2, 5 2 1 3, 5 2 3 1, 5 1 3 2, 5 1 2 3

The six different 4-digit numbers by fixing 8 in thousands place are 8 3 2 1, 8 3 1 2, 8 2 1 3, 8 2 3 1, 8 1 3 2, 8 1 2 3

To find:

To make six different 4-digit numbers by fixing 4 in thousands place.

To make four different 4-digit numbers by fixing 8 and 5 in the thousands place.

Solution:

We take the four numbers 1, 2, 3, 4.

By keeping the number 4 in the thousands place, we have 3 numbers to shuffle on 3 places without the repetition of the numbers. To find that, we have to take factorial of the total number of empty spaces i.e.,

$3 !=3 \times 2 \times 1 \Rightarrow 6$

So, totally 6 numbers can be formed by keeping the 4 in the thousands place and shuffling the other three numbers on the empty places.

And the numbers are,

$\Rightarrow$ 4 3 2 1, 4 3 1 2, 4 2 1 3, 4 2 3 1, 4 1 3 2, 4 1 2 3

Then, making of different four digit number by fixing 8 and 5 in the thousands place is same as that of the previous model of fixing the number 4 in the thousands place.

So, the answer is

$\Rightarrow$ 5 3 2 1, 5 3 1 2, 5 2 1 3, 5 2 3 1, 5 1 3 2, 5 1 2 3

$\Rightarrow$ 8 3 2 1, 8 3 1 2, 8 2 1 3, 8 2 3 1, 8 1 3 2, 8 1 2 3