Question

How many different 4-letter "words" can be formed from the letters in the word DUPLICATE?

Answer 1

`P_(9,4)=(9!)/((9-4)!)=(9!)/(5!)=(9xx8xx7xx6xx5!)/(5!)=3024`

Explanation:

A permutation means selecting a group of things (for instance, the 4 things) from a larger pool (for instance, the 9 letters) and doing so in such a way where order matters (so ABCD is different than DCBA - this is as opposed to a combination where order doesn't matter ABCD and DCBA are the same).

We can use the permutation formula:

`P_(n,k)=(n!)/((n-k)!); n="population", k="picks"`

And so:

`P_(9,4)=(9!)/((9-4)!)=(9!)/(5!)=(9xx8xx7xx6xx5!)/(5!)=3024`