Question

Number of integers between 1000and 4000 which can be formed using the digits 1,2,3 and 4. Of each digit is used more than once.

Answer 1

The total numbers of integers formed  between 1000 and 4000 are 191.

Step-by-step explanation:

Given:

Number of integers between 1000 and 4000.

Formed using the digits 1,2,3 and 4. Of each digit is used more than once.

To Find:

The total numbers of integers formed  between 1000 and 4000.

Solution:

As given,number of integers between 1000 and 4000.

$1000 < Numbers < 4000$.

As given,formed using the digits 1,2,3 and 4. Of each digit is used more than once.

There are four  digits 1,2,3,4.

At unit place  can be placed either 1,2,3, or 4.

If at first place 1 is placed, then rest three places can be filled by 4 digits in $4\times 4 \times\ 4 \ ways = 64\ ways.$

But we need to exclude 1000, hence, total numbers $=64-1=63$.

Again, if  at first place 2 is placed, then we can fill other 4 digits by  $4\times 4 \times\ 4 \ ways = 64\ ways.$

Again, if  at first place 3 is placed, then we can fill other 4 digits by  $4\times 4 \times\ 4 \ ways = 64\ ways.$

It required the numbers formed,less than 4000, therefore, there will be only 0 possible way.

The total numbers of integers formed  between 1000 and 4000 $=63+64+64= 191.$

Thus,the total numbers of integers formed  between 1000 and 4000  is 191.

# SPJ2