Question

how many 5-digit even numbers can be formed with the digits 1,2,3,4,5, and 6 if repetition is allowed?​

Answer 1

Given:

The given digits are 1,2,3,4,5, and 6.

To find:

The number of 5-digit even numbers that can be formed by using the given digits (if repetition is allowed).

Solution:

To form an even number, we need multiples of 2 at ones place.

In the given digits 2,4,6 are even number. So, the possible ways for the ones place is 3.

We have six given digits and repetition is allowed. So, the number of possible ways for each of the remaining four places is 6.

Total number of ways to form a 5 digit even number is:

$Total=6\times 6\times 6\times 6\times 3$

$Total=3888$

Therefore, total 3888 five-digit even numbers can be formed by using the given digits if repetition is allowed.