Math Is Fun Forum

chetah

Member

Registered: 2008-02-15

Posts: 32

Discrete math

A committee of 12 is to be selected from 10 men and 10 women.  In how many ways can the selection be carried out if

1 There are no restrictions
2 There must be six men and six women
3 There must be more women than men
4 There must be at least eight men?

LuisRodg

Real Member

Registered: 2007-10-23

Posts: 322

Re: Discrete math

1) If there are no restrictions then you need to choose 12 out of 20. --- 20C12

2) 6 men and 6 women. 12C6 + 12C6

and I dont know how to do to 3 and 4.

Im a Discrete math student myself and we just started to do combinatorics and permutations so maybe my 2 answers are wrong and I'd like to know the answer to the last parts.

mathsyperson

Moderator

Registered: 2005-06-22

Posts: 4,900

Re: Discrete math

For 2), you want 10C6 instead of 12C6. Also, they're multiplied instead of added.

For 3 and 4, I think you have to work out specific cases and add them all up.
So for 3), you'd work out the number of possible combinations that contain:

- 7 women and 5 men
- 8 women and 4 men
- 9 women and 3 men
- 10 women and 2 men

Then add those four values together to get an answer.

4) can be done similarly.

---

Why did the vector cross the road?
It wanted to be normal.