# What are the Permutations of the word 'Saskatchewan'?

1. Oct 10, 2004

### Dooga Blackrazor

I missed the day when my teacher went over Permutations. If someone could help me with the questions below, that would be great.

What are the Permutations of the word "Saskatchewan"?

10 PrN(right?) 6 = The amount of different ways 10 units can be organized into 6 units?

6! = 6 x 5, 6 x 4 ...... 6 x 1

8! / 9! = ? What is the purpose of using this and what does it mean?

Thanks~

2. Oct 10, 2004

### Sirus

You must account for the repetitions of letters in the word.

3. Oct 10, 2004

### HallsofIvy

Staff Emeritus
"Saskatchewan" has 12 letters. If they were all different, the answer would be 12!

However, three of the letters are "a", 2 of the letters are "s" (we don't treat the "S" and "s" as different, do we?) so we could swap the "a"s around without changing the actual word- there are 3! ways to do that. Since we don't want to count those as different, we need to divide by 3! to cancel those. There are 2! ways swap only the "s"s so we also need to divide by 2!: The total number of ways to permute "Saskatchewan" is 12!/(3!2!) (or 12!/3! if the "S" and "s" are considered different.

No, 6! is not what you say: 6!= 6x 5x 4x 3x 2x 1 = 720.

8!/9! = 8x7x6x5x4x3x2x1/9x8x7x6x5x4x3x2x1= 1/9 since everything else cancels out.

I have no idea what your purpose is in using it!

4. Oct 10, 2004

### Dooga Blackrazor

How many ways can the letters of the following words be arranged?