How many different seven-letter arrangements of the letters in the
word hexagon can be made if each letter is used only once?
(1) 28 (3) 720
(2) 49 (4) 5040

Use permutations which is also the slot meathod so exg
if you have the letters abc, then how many ways can you arrangge them with no repreats?
3 choices for the 1st slot
2 choices for the 2nd slot since 1 was used in 1st slot
3 choices for 3rd slot since 2 were used in previous slots so basically 3 times2 times 1 or 6

in this case of HEXAGON
7 letters so
7 times 6 times 5 times 4 times 3 times 2 times 1=answer=5040 ways

2(9+12)

2(9) + 2(12)

18 + 24

42

Let me know if this helps!