## anonymous one year ago MEDAL!! -COMBINTATIONS AND PERMUTATIONS- There is a new game show on television, 'Know Your Partner.' The producers must pick 4 people to participate in the pilot episode, so they bring in 8 male actors and 10 female actors to interview to participate. How many different combinations of contestants can be made from these actors?

1. jim_thompson5910

Do they care if they pick all guys? or all girls? or do they want it set up where they pick 2 guys and 2 girls?

2. jim_thompson5910

If you just want 4 people, out of a pool of 10+8 = 18, then you will need to compute 18 C 4 use the combination formula

3. anonymous

Doesn't specify, but i'm guessing 2 and 2

4. jim_thompson5910

or if you go with the 2 guys, 2 girls option, then you'll need to compute 8 C 2 and 10 C 2 then multiply those results

5. jim_thompson5910

The combination formula is $\Large _n C _r = \frac{n!}{r!*(n-r)!}$

6. anonymous

1,260 is what I came up with

7. jim_thompson5910

I'm getting 1,260 as well if you go with the 2 guys, 2 girls option

8. ganeshie8

@ikileyxx I think if it doesn't specify explicitly, it is better to go with just "4 persons"

9. jim_thompson5910

ganeshie8 may be right

10. anonymous

So 3,060 if "4 persons" correct?

11. jim_thompson5910

correct

12. anonymous

What if they only want males to participate in the episode? Then how many different combinations of contestants can be made from these actors?

13. jim_thompson5910

Then you will compute 8 C 4

14. jim_thompson5910

since there are 4 slots to fill from a pool of 8 guys

15. anonymous

thanks so much, big help

16. jim_thompson5910