## anonymous one year ago For The Questions, a club has 10 members. a. Find the number of different slates of 3 officers (list of president, vice-president, and treasurer) that the club could have for officers. b.Find the number of different slates of 4 officers (list of president, vice-president, secretary, and treasurer) that the club could have for officers.

1. anonymous

Are you studying combinations and permutations?

2. anonymous

Yes

3. anonymous

Is this question a combination or a permutation? What do you think?

4. anonymous

Remember that order doesn't matter in a combination but order does matter in a permutation.

5. anonymous

i think the first one is a permutation

6. anonymous

Right you are. In fact, they both are. Can you see that?

7. anonymous

Yes, because they have to be in a certain order, right?

8. anonymous

So, in the first question, you need to calculate$_3 P_{10}$Can you do that?

9. anonymous

I'm not sure how too

10. anonymous

Actually, my notation was backwards. Sorry. The general equation for permutations is$_{n}P_r=\frac{ n! }{\left( n-r \right) !}$And in the first question n=10 and r=3. Can you take it from here?

11. anonymous

I got -2 that's probably not correct is it?

12. anonymous

Not quite. The equation becomes$_{10}P_3=\frac{ 10! }{ 7! }$If you write out the factorial multiplications you'll see that all the factors from 7 down will cancel.

13. anonymous

Something like$_{10}P_3=\frac{ 10\times9\times8\times7\times6\times5\times4\times3\times2\times1 }{ 7\times6\times5\times4\times3\times2\times1}$

14. anonymous

See. Everything from 7 down will cancel out leaving$_{10}P_3=10\times9\times8=?$

15. anonymous

720? that's what I got from the multiplication

16. anonymous

Excellent. Now try the second question by yourself. You need to calculate$_{10}P_4$

17. anonymous

5040?

18. anonymous

Terrific. Well done.

19. anonymous

Thanks!

20. anonymous

You're welcome