A longer but elaborate method: (From

Math Forum)

Let's use a code to solve this problem. We have the following letters:

C

F

O

S

U

And we will take all the permutations of these letters and arrange

them in alphabetical order.

I think it will be helpful to think of these letters as numbers. The

first letter, alphabetically, in this list is C, so let's replace "C"

with the number 1.

The second letter is F, so let's replace it with 2.

And so on.

Using this code, the word "FOCUS" will be the sequence:

2 3 1 5 4

The first permutation in the sequence "alphabetically" is:

1 2 3 4 5

Then

1 2 3 5 4

Then

1 2 4 3 5

And it goes on like that.

The permutation we want is, again:

2 3 1 5 4

Which starts with a 2, so it comes AFTER every permutation that starts

with a 1. How many permutations start with a 1? The answer to that is

the number of ways the digits:

2 3 4 5

can be arranged.

tells us that that number of combinations is going to be 4! (4*3*2*1)

or 24.

So there are 24 permutations that begin with 1. That means that the

25th permutation is:

2 1 3 4 5

Now we've gotten the first digit in place. The next digit we want is

3. So we are going to have to work through all of the permutations

that start with "2 1". How many are there? 3! (3*2*1) or 6.

So the 30th permutation is:

2 3 1 4 5

And the 31st permutation is:

2 3 1 5 4