Find the number of 5 digit even numbers formed by the digits 0,1,2,3, 4 without repetition of digits

How many 5 digit even numbers can be made if: repetition is not allowed and 4 must be included.

Nội dung chính

• How many numbers of 5 digits can be formed with the digits 0 2 3 4 and 5 if the digits many repeat?
• How many five digit even numbers can be formed using 6 3 0 2 and 1 only once?
• How many 5 digit even numbers with distinct digits can be formed using the digits 1,2 5 5 and 4?
• How many 5 digit numbers can be formed when even repetition is allowed?

Use the indirect method to do this:

So basically i believe , you have to find the # of ways, 5 digit even #s that can be made, then subtract it from even numbers that do not include 4.

but i don't know how to act on my plan, how can i find how many 5 digit even numbers there are. and how can i find the number of ways that do not include 4 , but are even numbers?

grapz said:

How many 5 digit even numbers can be made if: repetition is not allowed and 4 must be included.

The first question is what is considered a five digit number?

Is 4=00004 considered such a number? If so the answer is \(\displaystyle \left( 5 \right)\left( {10^4 } \right)\).

If the first digit must be at least 1, example 10400, then the answer is \(\displaystyle \left( {10^4 } \right) + \left( 8 \right)\left( 4 \right)\left( {10^3 } \right)\).

hm

the defination of a 5 digit number in this case would be for the first number to be at least one. but, repetition is not allowed. i believe the method u shown here allows repetition.

grapz said:

a 5 digit number in this case would be for the first number to be at least one. but, repetition is not allowed.

In that case the answer is \(\displaystyle \left( 9 \right)\left( 8 \right)\left( 7 \right)\left( 6 \right) + \left( 8 \right)\left( 4 \right)\left( 8 \right)\left( 7 \right)\left( 6 \right)\).

Count those beginning with a 4 and add those that do not.

thanks.

So this is now what i did.

The question was, how many 5 digit even numbers can be made if repetition is not allowed and the number four must be included.

so i did 8 x 8 x 7 x 6 x 4 - 7 x 7 x 6 x 5 x 3 = 6342. but the answer is 7686.

8x8x7x6x4- thats the number of 5 digit even numbers, with no repetition.

and 7x7x6x5x3 is when 4 is excluded.

grapz said:

The question was, how many 5 digit even numbers can be made if repetition is not allowed and the number four must be included.
the answer is 7686.

Are you saying that the answer is 7686?
If so, then your answer key is just wrong!
The correct answer is 13776.

There are 3024 five-digit numbers that begin with the digit 4 with no repetition.
So can you understand how many more there are?