Question

How many permutations are there of the letters in the word 'PLANTS', if all the letters are used without repetition?

Answer 1

Answer:

6!

or

6*5*4*3*2*1

or

720

Step-by-step explanation:

The word 'PLANTS' contains no letter more than once.

It is say 6 letter word.

_  _  _ _ _ _

There are 6 ways to choose the first blank (after than there are 5 letters left to choose from)

After the first blank, there are 5 letter left to choose from so there are 5 ways to choose the second blank.

Then 4 ways for the third blank.

3 ways for the fourth blank.

2 ways for the fifth blank.

1 way for the sixth blank.

Now to figure out the number of permutations you must multiply the number of different ways we have above for each blank.

That is we are doing 6*5*4*3*2*1 or 6!