candy store problem

[zofaan]

Here is a question I wrote. I want to make sure it's correct. Anyone get it?

10 people go to a candy store in order for each to select 1 among 10 flavors of ice cream. Assuming each of flavor is equally likely to be selected by each person and each flavor can be selected by more than 1 person, what is the probability that exactly 3 people select the same flavor while the other 7 each select a flavor unique to himself?
(A) (10 choose 3)(10 choose 7)(10! / 2) ÷ (10^10)
(B) (10 choose 3)(10 choose 7)(9! / 2) ÷ (10^10)
(C) (10 choose 3)(10 choose 7)(9! / 2) ÷ (10!)
(D) (10 choose 3)(10! / 2) ÷ (10^10)
(E) (10 choose 3)(9! / 2) ÷ (10^10)

 

[pka]

10 people go to a candy store in order for each to select 1 among 10 flavors of ice cream. Assuming each of flavor is equally likely to be selected by each person and each flavor can be selected by more than 1 person, what is the probability that exactly 3 people select the same flavor while the other 7 each select a flavor unique to himself?

It does appear to me as if any of those are correct.

I get the the probability is \(\displaystyle \dfrac{\left[10\cdot\dbinom{10}{3}\right]\dfrac{9!}{2}}{10^{10}}\).

That may be one of yours that I misread.

 

[zofaan]

No that's right. That's the same as (D)
Ok thanks for the confirmation.