## anonymous 5 years ago There are 10 members of a committee. One will be chosen as President, one as Vise President, one as Treasurer, and one as Secretary. In how many different ways can those offices be filled if the same person cannot serve in more than one office at the same time? a) 10!/4!6! b) 10!/4! c) 10! d) 10!/6!

1. anonymous

10! / 4 !

2. anonymous

How do you figure?

3. anonymous

there are 10 ways to choose president. for each choice of president, there are 9 choices left for vice president, then 8 choices left for vice president ... 10*9*8*7

4. anonymous

oh it should be d)

5. anonymous

nPr = n! / ( n-r)!

6. anonymous

10*9*8*7 = 10*9*8*7 * 6! / 6!

7. anonymous

i think maybe no.

8. anonymous

no

9. anonymous

oops you are right sorry

10. anonymous

10*9*8*7

11. anonymous

it is just that $\frac{10!}{6!}$ is a silly way to write that

12. anonymous

my mistake laplace is right and i am wrong