# Assistance with permutation.

• Oct 9th 2010, 11:19 AM
Squared
Assistance with permutation.
Hey everyone, I need to acquire an explanation concerning a question I encountered
with statistics. Here it is:

How many even numbers greater than 50000 can be made with the digits 3, 4, 5, 6, 7, 0 without repeating any of the digits?

The book lists the answer as 504 but I need an explanation as to how this answer is attained. If someone could explain it, I'd be very grateful. (Hi)

Thanks.
• Oct 9th 2010, 12:06 PM
Plato
Quote:

Originally Posted by Squared
How many even numbers greater than 50000 can be made with the digits 3, 4, 5, 6, 7, 0 without repeating any of the digits?

Assuming you mean all five digit even numbers greater than 50000 along with all six digit even numbers then the given answer is correct.
Start with the five digit numbers ending in 0: there are $3\cdot 4!$ of those.
The five digit numbers ending in 4: there are $3\cdot 4!$ again.
But five digit numbers ending in 6: there are $2\cdot 4!$ of those. Because we can use only the 5 or 7 as the first digit.
That gives 192 five digit even numbers greater than 50000.

Now you count the six digit even numbers
Remember, they cannot have a 0 in the first place.