Permutation and combination

Question

There are 5 doors to a lecture room. In how many ways can a student enter the room through a door and leave the room by a different door?

Answer 1

doors A, B, C, D, E

enter through A and leave through B, C, D, or E for a total of 4 ways

 

enter through B and leave through A, C, D, or E for a total of 4 ways

 

enter through C and leave through A, B, D, or E for a total of 4 ways

 

enter through D and leave through any one of the other 4 doors for 4 more ways

 

enter through E and leave through any one of the other 4 doors for 4 more ways

 

5*4=20 ways

Answer 2

twenty