how many ways can the letters of the word "capital" be arranged if the first letter of the word has to be "P"

Question

anonymous · Answer

_ _ _ _ _ _ _
There are 7 spaces to fill, but we know the first letter has to be P.
P _ _ _ _ _ _
So we have to figure out how many options there are for each of the remaining spaces.

If the first letter is determined already, how many options do we have for what the second letter can be?

qemargray6 · Answer

6?

anonymous · Answer

Correct!  So lets say we take one of those options away to fill that second space...then how many options for the next letter?

Here's what we have right now:  1 option for the first letter (since it has to be P), 6 options for the second letter...
1 x 6 x _ x _ x _ x _ x _

qemargray6 · Answer

5 and then 4 and then 3 and then 2

anonymous · Answer

Yes!  Then 1 for the last one.  So to find the answer you just have to multiply all of those numbers.

qemargray6 · Answer

720?

anonymous · Answer

Yes!