## 4-digit positive integers

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### 4-digit positive integers

by ska7945 » Fri Aug 22, 2008 11:16 pm
How many 4-digit positive integers are there in which all 4 digits are even?

A. 625
B. 600
C. 500
D. 400
E. 256

oa c
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### Re: 4-digit positive integers

by sudhir3127 » Fri Aug 22, 2008 11:22 pm
ska7945 wrote:How many 4-digit positive integers are there in which all 4 digits are even?

A. 625
B. 600
C. 500
D. 400
E. 256

oa c
C 500

to be an even number we have to take into consideration only 0,2,4,6,8

first digit can be formed in 4 ways( cant take 0 )
next 3 digits out of 5 in 5^3 ways

thus its
4*5^3 = 500

hope it helps..

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by carefreeamit » Fri Aug 22, 2008 11:22 pm
4 digit number means it should be >= 1000 and <= 9999.
The first place can be taken by 2,4,6,8 i.e. in 4 ways.
The second, third & fourth place can be taken by 0,2,4,6,8 i.e. 5 ways each.
So the number of positive integers will be = 4*5*5*5 = 500

Ans C.

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### Re: 4-digit positive integers

by [email protected] » Fri Apr 16, 2021 7:33 am
ska7945 wrote:
Fri Aug 22, 2008 11:16 pm
How many 4-digit positive integers are there in which all 4 digits are even?

A. 625
B. 600
C. 500
D. 400
E. 256

oa c
Solution:

The even digits are 0, 2, 4, 6, and 8. However, since the first digit (or the thousands place digit) can’t be 0, there are 4 choices for the thousands digit, while the other three places (hundreds, tens, and units) have 5 choices each. Therefore, the total number of 4-digit numbers with all even digits is 4 x 5 x 5 x 5 = 500.