Now, let's suppose you only want to choose a few
letters out of your word.
For example, you only
want to choose 2 letters out of the word "TABLE".
Here are all the ways to pick them:
TA TB TL TE AT AB AL AE BT BA
BL BE LT LA LB LE ET EA EB EL
There are 20 pairs.
Is there a rule here too? Of course there is:
1. There are 5 ways to choose the first letter.
2. After you choose the first letter,
there are 4 ways to choose the
So, the number of 2 letter permutations
of the 5 letter word "TABLE" is 5 x 4 = 20
How about a general rule? Here it is:|
If you have a word with "N" letters in it,
and you only want to pick a few letters from it, then:
N = 5 letters
|2||N x (N-1)||5 x 4 = 20
|3||N x (N-1) x (N-2)||5 x 4 x 3 = 60
|4||N x (N-1) x (N-2) x (N-3)||5 x 4 x 3 x 2 = 120
Using factorials, this is:
P = N! / (N - M)!
where M is the number of letters you are selecting.
For our example of 3 letters out of the word TABLE, this becomes:
P = 5! / (5-3)! = 120 / 2! = 120 / 2 = 60 ways.