Solving Combinations Problem: 7 0s & 3 1s

[amcavoy]

How many sequences are there consisting of seven 0's and three 1's? Example: 0101010000

I was thinking that I could solve this with combinations. However, I am unsure of how to use it in this case. If I remember correctly, the combinations are given by:

\begin{pmatrix}n \\ r\end{pmatrix}=\frac{n!}{r!\,\left(n-r\right)!}

Hmm. Any thoughts on this? Am I on the right track with the above?

Thanks.

 

[Tide]

There are 2^{10} ways of selecting the digits and _{10}C_3 ways of having three 1's.

 

[amcavoy]

There are 2^{10} ways of selecting the digits and _{10}C_3 ways of having three 1's.

Alright. I was thinking that it didn't matter if they were the same number; I could still use the formula above. Thanks for the confirmation .