#### leehuan

##### Well-Known Member

- Joined
- May 31, 2014

- Messages
- 5,805

- Gender
- Male

- HSC
- 2015

A group of 12 people is to be divided into discussion groups.

(i) In how many ways can the discussion groups be formed if there are 8 people in one group, and 4 people in another?

(ii) In how many ways can the discussion groups be formed if there are 3 groups containing 4 people each?

So the answer to part (i) is \binom{12}{8} which is kinda trivial

The answer to part (ii) is \binom{12}{4}*\binom{8}{4} / 3!. I eventually convinced myself that the division by 3! was because of repetition/double counting from the ordering being unimportant.

But then I had a look at part (i) again and I got confused. Suddenly I'm not sure why division by 1/2! was not necessary for part (i) whereas division by 1/3! was necessary for part (ii). Clarification please?