Okay, I think I'm too sleepy to study, I need to take a nap before I want to keep continuing this stuff, see ya : )

We know choosing 3 people from 5 people is like 5 x 4 x 3 = 60.

Well, thinking in other way with repetitions allowed, then total number of ways from choosing 3 people from 5 is like 5 x 5 x 5 = 125, then minus triplets which are two types, AAA and BBB

first type, AAA: there are 5 ways of it (AAA through EEE)

second type, AAB: there are 5 ways to choose the repeated AA, and 4 ways to choose B,

then between AAB, there are 3 ways of arranging it. AAB, ABA and BAA

so 5 x 4 x 3=60

then 125- 5-60= 60, which are the same as 5 x 4 x3=60

awesome!!!

Use N instead of 5

first type: N

second type: N (N-1)x3= 3N2-3N

then N3-3N2-3N+N= N (N-1)(N-2)

Awesome!!!

I know today may not be perfect, be patient to it, you will be fine, Wallace Tiger : )