Question

The letters A, N, T, and O are on a table. In how many ways can these letters be arranged?
A.
1
B.
4
C.
12
D.
24

Answer 1

if you're talking from left to right, then think of it like this...
you have 4 spots. how many letters do you have to choose from to put into the first spot?

after you've selected one, how many reamin to go into the 2nd spot? and so on.

you have to multiply those numbers because of the multiplication principle.

what do you get?

Answer 2

D

Answer 3

yep. anytime you arranging (i.e., order matters) it's a permutation. in this case you have 4 objects taken 4 at a time, that's \(_4P_4 = 4!\)