If all the numbers have to be used each time then there are 9 ways of choosing the first number. After that there are 8 ways of choosing the second number. This presumes that we can't use the same number in two different places in the one arrangement. Say we choose 4 as the first number, the second could be any of 1,2,3,5,6,7,8 or 9 Already we have 72 permutations and we've only got the first two numbers sorted. We not have 7 numbers left from which to choose the third, and so on. To go all the way down to the last number we end up with 9 x 8 x 7 x 6 x 5 x 4 x 3 x 2 x 1 permutations. Work it out, it's a big number.
120 ways
How many different ways can we arrange 9 objects taken 3 at a time?
In 6 way
120
4! = 4 * 3 * 2 * 1 = 24 ways[1]
8! = 40320 ways.
4
24
One... numbers
you can arrange 8 pictures 28 different ways
24 ways
you can arrange three beads 9 different ways.
120 ways
7!=5040
8
Only One
There are six, but it is traditional to list them least to greatest,