How many different arrangements of all the letters of the word CAPITOL begin with the letter C? (Each letter is used exactly once.)
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → 720
With the first place fixed as C, only the remaining letters are arranged, in the places after it.
CAPITOL has 7 different letters
C is fixed in the first place, so 6 letters remain for 6 places
Arrangements \(=6!=6\times5\times4\times3\times2\times1=720\)
Why the other options are incorrect
Option (1) 5040 — Incorrect. This is \(7!\), the count of all arrangements, without fixing C first.
Option (3) 120 — Incorrect. This is \(5!\); after fixing C there are 6 letters left, not 5.
Option (4) 4320 — Incorrect. This is \(6\times6!\); the first place has only one choice, C.