Permutations & Combinations

  • #1
What would be the best way to solve for n if 10Pn = 90?
Also, how would you solve this problem:
In a student council election, there are 3 candidates for president, 3 for secretary, and 2 for treasurer. Each student may vote for at least one position. How many ways can a ballot be marked?
Thanks in advance.
 

Answers and Replies

  • #2
789
4
For the first one, use the fact that [tex]_{n} P _{k} = \frac{n!}{(n-k)!}[/tex]
 
  • #3
I used that and multiplied both sides by (10 - n)!, then divided both sides by 90. Then I got 40320 = (10 - n)!. But that's where I got stuck.
 
  • #4
2,209
1
Try expressing 40320 as a factorial.
 
  • #5
I suppose it would be 8! = (10 - n)! then? Still don't know what to do...
 
  • #6
2,209
1
if 8! = (10-n)!
n has to equal 2.
 
  • #7
Oh, I see now.. don't know why I didn't before. Thanks!
 

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