Permutation questions help?!!!!!!

I need help on the following questions, its from my friends previous test and i'm so lost...:?

1. In how many ways can 7 people be seated at a circular table if Homer, Bart and Lisa must sit together?

2. How many four letter arrangements are there using only letters of the word HAPPY?

3. How many integers between 100 and 999 have different digits?

4. How many integers between 100 and 999 inclusive consists of different odd digits?

5. How many 7 digit even numbers less than 5,000,000 can be formed using all the digits 1,2,2,3,5,5,6?

Thanks alot! It would help alot if someone can explain their answers too...!

Never been exposed to permutations?

Nope..but I just have problem with number 1 and 5 now.


The answer for number 1 is supposedly (5-1)!-3!= 18 but why is that?

Also for number 5 is it 4.6.5.4.3.2.1./2!2!= 720?