Question

In how many ways can the letters of the word "company" be rearranged? How many of those arrangements start with the letter P?

Answer 1

`7! = 5040` in total. `6! = 720` start with P.

Explanation:

The formula for a permutation is:

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

however, if we are doing a permutation with all the elements (so that `k=n`), it simplifies to:

`n!`

The word company has 7 letters and they are all different, and so we can say that the number of permutations that can be made is:

`7! = 5040`

(we can see this by realizing that any one of the seven letters can be in place A, than any of the remaining six can be in place B, and so on down to the last place).

How many of these start with the letter P? We can figure this out by seeing that if we force P to be the first letter, the remaining 6 letters can be in any of the remaining positions, and so we have:

`6! = 720`