Counting Problem Help

Apr 2010
15
2
1) How many ways would you be able to hand out 10 identical invitations to your party if you have 15 friends, assuming they can't receive more than one invitation?

My answer: \(\displaystyle 15!/10! = 15*14*13*12*11 \)
but this seems really off to me.

2) If you and your 10 friends at party (11 total) play 6 different games with 1 game winning prize for each game (prize is the same for each game), how many ways can the prizes be handed out if someone can receive more than one prize?

So we have:
11 people and 6 identical prizes based on this problem

Is this a selection problem? :/
 

Plato

MHF Helper
Aug 2006
22,455
8,631
1) How many ways would you be able to hand out 10 identical invitations to your party if you have 15 friends, assuming they can't receive more than one invitation?
My answer: \(\displaystyle 15!/10! = 15*14*13*12*11 \)
but this seems really off to me.
You are quite a bit off: \(\displaystyle ^{15}\mathcal{C}_{10}=\binom{15}{10}=\frac{15!}{10!(5!)}\).
You select 10 friends from 15 to get an invitation.