probablity question on lottery In a lottery,out of $1000$ tickets there are $5$ tickets having some prize on it.
1)If $5$ tickets were purchased,what is probability of winning all $5$ prize tickets?
2)If $10$ tickets were purchased,what is probability of winning all $5$ prize tickets?
Although I've tried like this..
1)$\displaystyle P=\frac{\binom{5}{5}}{\binom{1000}{5}}$
but it seems wrong.
2)$\displaystyle P=\frac{\binom{10}{5}}{\binom{1000}{5}}$
 A: Use the Hypergeometric distribution. If a random variable $X$ has Hypergeometric distribution: $X \stackrel{d}{=}Hg(n,R,N)$. Where $N$ is the size of the population, $n$ is the sample you take, and $R$ is the number of individuals from the population with the characteristic you are looking for. Then we have:
$$P(X=x)=\frac{\binom{R}{x}\binom{N-R}{n-x}}{\binom{N}{n}}.$$
Where $x$ is the number of successes you want. In your case the characteristic is a winning ticket.
A: Your answer for #1 is correct. Note that $\begin{pmatrix} 5 \\ 5\end{pmatrix} = 1$, so $$\require{cancel}\frac{\begin{pmatrix} 5 \\ 5\end{pmatrix} }{ \begin{pmatrix} 1000 \\ 5 \end{pmatrix} } = \frac{1}{\frac{1000!}{5! 995!}} = \frac{5!995!}{1000!} = \frac{5!\cancel{995!}}{1000 \cdot 999 \cdot 998 \cdot 997 \cdot 996 \cdot \cancel{995!}}$$
which is the same result as @sanjab's comment.
#2 is just a generalization of #1.
A: 1)P=5c5/1000c5
but it seems wrong.
2)purchasing 10 tickets means at least 5 of them is non-prize tickets.
p=(10C5 x 990C5)/1000C10.
I'm also not confident with this.
PS-C means taking combinations.
A: In a box there are 1000 balls in which 5 are red,995 are non-red.
(we don't bother with which non-red ie.blue,green,black--all colors other than red are taken as non-red here)
i)if 5 balls are drawn,find probability that all 5 drawn balls are red.
ii)if 10 balls are drawn,find probability that 5 balls are red among them.   
my 1st query is 
Are these questions are of same above pattern(see original lottery question).
or,will it differ?
 because those 1000 tickets(in above question) are of different types(let all labelled 1 to 1000)
and here in 1000 balls,5 red are identical and 995 non-red are identical.
Does this make any difference in solving.
