Question

How many even numbers can be formed if the digits of the number 112433 are rearranged?

Answer 1

.

Answer 2

60

Explanation:

To get an even number, we need the last digit to be even. There are 2 even numbers in the list (2, 4), and so we can have either one of those as the last number.

That leaves 5 numbers to arrange. If the numbers were all unique, we'd be able to say that the number of arrangements is `5!`. However, because there are duplicates of the 1s and 3s, we need to divide by the number of ways each can self order internally (which is the number of duplicate digits within each group, factorial).

This gives:

`2xx(5!)/(2!2!)`

`(5!)/(2!)=120/2=60`