Question

Using the given digits without repetition form the smallest and the greatest $4-\mathrm{digit}$ numbers.

$7,0,3,8$

Answer 1

Step I: Forming the smallest $4-\mathrm{digit}$ number.

The digits $7,0,3,8$ if written in the increasing order will give the smallest $4-\mathrm{digit}$ number.

The increasing order is $0,3,7,8$.

But, $0$ can't be written as the first digit as it will form a $3-\mathrm{digit}$ number, so we will place $0$ to the second position, that is after the second smallest digit.

Therefore, the smallest $4-\mathrm{digit}$ number is $3078$.

Step II: Forming the greatest $4-\mathrm{digit}$ number.

The digits $7,0,3,8$ if written in the decreasing order will give the greatest $4-\mathrm{digit}$ number.

The decreasing order is $8,7,3,0$.

Therefore, the greatest $4-\mathrm{digit}$ number is $8730$.

Hence, the smallest $4-\mathrm{digit}$ number is $3078$ and the greatest $4-\mathrm{digit}$ number is $8730$.