Using the digits 1, 2, 3, 4, 5, how many even three-digit numbers less than 500 can be formed if each digit can be used more than once?

Guest Apr 25, 2018

#2**+1 **

How in the world did you get that!!

There are: 4 numbers to choose from for the 1st digit from the left. Any number beginning with 5 is not allowed, because that number would be** over 500!!**

There are: 5 numbers to choose from for the 2nd digit from the left.

There are: 2 numbers to choose from for the 3rd and last digit.

So, that is: 4 x 5 x 2 =40 numbers in total.

Here are ALL the permutations possible:

{1, 1, 1} | **{1, 1, 2} **| {1, 1, 3} |** {1, 1, 4}** | {1, 1, 5} | {1, 2, 1} |** {1, 2, 2}** | {1, 2, 3} | **{1, 2, 4}** | {1, 2, 5} | {1, 3, 1} |** {1, 3, 2}** | {1, 3, 3} | **{1, 3, 4}** | {1, 3, 5} | {1, 4, 1} | **{1, 4, 2} **| {1, 4, 3} | **{1, 4, 4}** | {1, 4, 5} | {1, 5, 1} **| {1, 5, 2**} | {1, 5, 3} | {**1, 5, 4}** | {1, 5, 5} | {2, 1, 1} |** {2, 1, 2}** | {2, 1, 3} | **{2, 1, 4}** | {2, 1, 5} | {2, 2, 1} | {2, **2, 2}** | {2, 2, 3} | **{2, 2, 4}** | {2, 2, 5} | {2, 3, 1} | {**2, 3, 2**} | {2, 3, 3} |** {2, 3, 4}** | {2, 3, 5} | {2, 4, 1} | **{2, 4, 2}** | {2, 4, 3} | **{2, 4, 4**} | {2, 4, 5} | {2, 5, 1} | **{2, 5, 2}** | {2, 5, 3} | {**2, 5, 4}** | {2, 5, 5} | {3, 1, 1} | {**3, 1, 2}** | {3, 1, 3} | **{3, 1, 4}** | {3, 1, 5} | {3, 2, 1} | **{3, 2, 2}** | {3, 2, 3} | **{3, 2, 4} **| {3, 2, 5} | {3, 3, 1} | **{3, 3, 2}** | {3, 3, 3} | **{3, 3, 4}** | {3, 3, 5} | {3, 4, 1} | **{3, 4, 2}** | {3, 4, 3} | **{3, 4, 4} **| {3, 4, 5} | {3, 5, 1} | **{3, 5, 2}** | {3, 5, 3} | {3, **5, 4}** | {3, 5, 5} | {4, 1, 1} | **{4, 1, 2}** | {4, 1, 3} |** {4, 1, 4} **| {4, 1, 5} | {4, 2, 1} | {**4, 2, 2}** | {4, 2, 3} | **{4, 2, 4}** | {4, 2, 5} | {4, 3, 1} | {**4, 3, 2}** | {4, 3, 3} | **{4, 3, 4} **| {4, 3, 5} | {4, 4, 1} | **{4, 4, 2}** | {4, 4, 3} | **{4, 4, 4}** | {4, 4, 5} | {4, 5, 1} | **{4, 5, 2}** | {4, 5, 3} |** {4, 5, 4}** | {4, 5, 5} |. These are ALL the permutations with repeats under 500. If you count the **bold ones** you should get** 40.**

Guest Apr 25, 2018

edited by
Guest
Apr 25, 2018

edited by Guest Apr 25, 2018

edited by Guest Apr 25, 2018

edited by Guest Apr 25, 2018

edited by Guest Apr 25, 2018

#1**+2 **

The only digit we have restictions for is the last one, it must be even.

The other digits in the number ABCDE have no restrictions and can be any one of the 5.

There are only two even numbers in the list, so there are 2 choices for the last digit.

The other 4 digits have no restrictions, and since the problem allows repeats, there are 5 choices.

The final answer is:

\(5^4\cdot2=\boxed{625}.\)

I hope this helped.

Gavin

GYanggg
Apr 25, 2018

#2**+1 **

Best Answer

How in the world did you get that!!

There are: 4 numbers to choose from for the 1st digit from the left. Any number beginning with 5 is not allowed, because that number would be** over 500!!**

There are: 5 numbers to choose from for the 2nd digit from the left.

There are: 2 numbers to choose from for the 3rd and last digit.

So, that is: 4 x 5 x 2 =40 numbers in total.

Here are ALL the permutations possible:

{1, 1, 1} | **{1, 1, 2} **| {1, 1, 3} |** {1, 1, 4}** | {1, 1, 5} | {1, 2, 1} |** {1, 2, 2}** | {1, 2, 3} | **{1, 2, 4}** | {1, 2, 5} | {1, 3, 1} |** {1, 3, 2}** | {1, 3, 3} | **{1, 3, 4}** | {1, 3, 5} | {1, 4, 1} | **{1, 4, 2} **| {1, 4, 3} | **{1, 4, 4}** | {1, 4, 5} | {1, 5, 1} **| {1, 5, 2**} | {1, 5, 3} | {**1, 5, 4}** | {1, 5, 5} | {2, 1, 1} |** {2, 1, 2}** | {2, 1, 3} | **{2, 1, 4}** | {2, 1, 5} | {2, 2, 1} | {2, **2, 2}** | {2, 2, 3} | **{2, 2, 4}** | {2, 2, 5} | {2, 3, 1} | {**2, 3, 2**} | {2, 3, 3} |** {2, 3, 4}** | {2, 3, 5} | {2, 4, 1} | **{2, 4, 2}** | {2, 4, 3} | **{2, 4, 4**} | {2, 4, 5} | {2, 5, 1} | **{2, 5, 2}** | {2, 5, 3} | {**2, 5, 4}** | {2, 5, 5} | {3, 1, 1} | {**3, 1, 2}** | {3, 1, 3} | **{3, 1, 4}** | {3, 1, 5} | {3, 2, 1} | **{3, 2, 2}** | {3, 2, 3} | **{3, 2, 4} **| {3, 2, 5} | {3, 3, 1} | **{3, 3, 2}** | {3, 3, 3} | **{3, 3, 4}** | {3, 3, 5} | {3, 4, 1} | **{3, 4, 2}** | {3, 4, 3} | **{3, 4, 4} **| {3, 4, 5} | {3, 5, 1} | **{3, 5, 2}** | {3, 5, 3} | {3, **5, 4}** | {3, 5, 5} | {4, 1, 1} | **{4, 1, 2}** | {4, 1, 3} |** {4, 1, 4} **| {4, 1, 5} | {4, 2, 1} | {**4, 2, 2}** | {4, 2, 3} | **{4, 2, 4}** | {4, 2, 5} | {4, 3, 1} | {**4, 3, 2}** | {4, 3, 3} | **{4, 3, 4} **| {4, 3, 5} | {4, 4, 1} | **{4, 4, 2}** | {4, 4, 3} | **{4, 4, 4}** | {4, 4, 5} | {4, 5, 1} | **{4, 5, 2}** | {4, 5, 3} |** {4, 5, 4}** | {4, 5, 5} |. These are ALL the permutations with repeats under 500. If you count the **bold ones** you should get** 40.**

Guest Apr 25, 2018

edited by
Guest
Apr 25, 2018

edited by Guest Apr 25, 2018

edited by Guest Apr 25, 2018

edited by Guest Apr 25, 2018

edited by Guest Apr 25, 2018

#3**+2 **

Using the digits 1, 2, 3, 4, 5, how many even three-digit numbers less than 500 can be formed if each digit can be used more than once?

The hundreds digit can be 1,2,3 or 4 that is 4 choice (less than 500)

the tens has 5 choices.

The units digit has to be even so that is 2 choices

so there are 4*5*2= 40 possible numbers

Melody
Apr 25, 2018