So I am stuck on part a for this problem:

> 
> Prove that C(n, 2k)C(2k, k) = C(n, k)C(n − k, k), where n ≥ 2k > 0, by using 
> 
> 
> 
> > 
> > (a) a combinatorial proof, 
> > 
> > 
> > (b) an algebraic proof
> > 
> > 
> > 
> 
> 
> 

for part a, I'm pretty confused on using combinatorial proofs but for b this is what i got:

```
C(n, 2k)C(2k, k) = C(n, k)C(n − k, k)
n!/[(2k)!(n-2k)!] * (2k)!/[k!(2k-k)!]  = n!/[k!(n-k)!] * (n-k)!/[k!(n - k -k)!]
n!/[(2k)!(n-2k)!] * (2k)!/[k!(k)!]  = n!/[k!(n-k)!] * (n-k)!/[k!(n - 2k)!]
1/[(2k)!(n-2k)!] * (2k)!/[k!(k)!]  = 1/[k!(n-k)!] * (n-k)!/[k!(n - 2k)!]
1/[(2k)!] * (2k)!/[k!(k)!]  = 1/[k!(n-k)!] * (n-k)!/[k!]
1/[(2k)!] * (2k)!/[k!(k)!]  = 1/[k!] * 1/[k!]
1/[(2k)!] * (2k)!  = 1
1 = 1
QED

```

where at the end I was able to show that they are the same. Please tell me if I am correct on b and how to do a using combinatorial proof method.