Question

What is the difference in the number of 5 digit numbers that can be formed from the digits 0-9 with replacement and without replacement?
​

Answer 1

Given : 5 digit numbers that can be formed from the digits 0-9

To Find : difference in the number of 5 digit numbers  that can be formed  with replacement and without replacement

Solution:

5 digit numbers that can be formed from the digits 0-9 with replacement

1st  Digit can be in  9 ways ( digits 1 to 9 )

Hence digit from 2nd place to 5th place can be in 10 ways Each

Hence total Possible numbers are :

9 * 10⁴

= 90,000

5 digit numbers that can be formed from the digits 0-9 without replacement

1st  Digit can be in  9 ways 1 to 9  

and remaining 4 digits out of remaining 9 digits cab be selected in

⁹P₄  ways = 3,024

Total possible = 9 x 3,024 = 27,216

difference in the number of 5 digit numbers that can be formed from the digits 0-9 with replacement and without replacement

=  90,000 - 27,216

= 62,784

Learn More:

How many 3-digit numbers can be formed from the digits 2, 3, 5, 8 and

https://brainly.in/question/21390194

how many different 6 digit numbers can be formed using digits in the ...

https://brainly.in/question/13738553

how many natural numbers less 4000 can be formed using digits 2,4 ...

https://brainly.in/question/14179408

Answer 2

SOLUTION

TO DETERMINE

The difference in the number of 5 digit numbers that can be formed from the digits 0-9 with replacement and without replacement

EVALUATION

Here we have to form 5 digit number from the digits 0 - 9

Here the number of digits is from 0 to 9

So the total number of digits = 9

With replacement

In this case we have 5 digits in the number. Now we can have any digit in the 5th place except 0 because 0 will cause the number to a 4 digit number

Hence the total number of 5 digit numbers

$= \sf{9 \times {10}^{4} }$

$= \sf{90000}$

Without replacement

In this case we have 5 digits in the number. Now we can not have 0 in 5th place because it will cause the number to a 4 digit number.

So 5 th place have 9 choices

4 th place have 9 choices

3rd place have 8 choices

2nd place have 7 choices

1st place have 6 choices

Hence in this case the total number of 5 digit numbers

= 9 × 9 × 8 × 7 × 6

= 27216

Hence the required difference

= 90000 - 27216

= 62784

FINAL ANSWER

The required difference = 62784

━━━━━━━━━━━━━━━━

Learn more from Brainly :-

1. A Cricket team squad has 15 members. In

how many ways a team of 11 members can

be selected such that one of the players

https://brainly.in/question/25139714

2. How many byes will be given if 32 teams are participating in a knock-out tournament

https://brainly.in/question/24215389