Probability and Statistics

[watchkimberly]

I'm struggling with this one. I think I have the first one.

The outcome of chance events in a fantasy role-playing game is determined by rolling polyhedral dice with anywhere from 4 to 20 sides. Suppose you roll a 16 sided die 5 times and observe the number on the top of the die.
a) How many possible outcomes are there for these 5 rolls? n=16 and k=6, 16C5 = 16P5/5! = 16*15*14*13*12/5*4*3*2*1 = 4,368
b) In how many of the outcomes in the part (a) do the 5 rolls produce five different numbers? This one I'm not to sure. So I think it's 16C5/5! * 5C5//5! ?
c) What is the probability that at least 2 of the rolls are the same?

 

[Harry_the_cat]

I'm struggling with this one. I think I have the first one.

The outcome of chance events in a fantasy role-playing game is determined by rolling polyhedral dice with anywhere from 4 to 20 sides. Suppose you roll a 16 sided die 5 times and observe the number on the top of the die.
a) How many possible outcomes are there for these 5 rolls? n=16 and k=6, 16C5 = 16P5/5! = 16*15*14*13*12/5*4*3*2*1 = 4,368
b) In how many of the outcomes in the part (a) do the 5 rolls produce five different numbers? This one I'm not to sure. So I think it's 16C5/5! * 5C5//5! ?
c) What is the probability that at least 2 of the rolls are the same?

a) What is k and why is it 6? I would say there would be 16^5 = 1 048 576 different outcomes. Your answer implies no repetitions and also implies 1,2,3,4,5 is the same outcome as 4,5,1,3,2.

 

[watchkimberly]

I was using the multiplication counting principle where nCk=nPk/k!

 

[Harry_the_cat]

But that's not applicable in this case, is it?

 

[pka]

The outcome of chance events in a fantasy role-playing game is determined by rolling polyhedral dice with anywhere from 4 to 20 sides. Suppose you roll a 16 sided die 5 times and observe the number on the top of the die.
a) How many possible outcomes are there for these 5 rolls?
b) In how many of the outcomes in the part (a) do the 5 rolls produce five different numbers?
c) What is the probability that at least 2 of the rolls are the same?

a) If you toss a sixteen sided die with a different value on each face five times:
then there are $16^5=1048576$ possible outcomes.
b) of those there $43680$ ordered $5$-tuples. { there are $4368$ unorder outcomes all different].