### Equations involving indices of binomial coefficients

I wanted to figure out which binomial coefficient would another sum of binomial coefficients be equal to. I tried to find that using the solve function in the following manner:

```
solve(binomial(1002,y) == sum(z*binomial((1001-z),950),z,1,51),y)
```

This did not yield the desired result evaluating the expression on the right side of the equation and printing the left side as it is as is shown below :

```
[binomial(1002, y) == 10480853106371895870377052872259391385423261386799458513700836377945732866106336546780]
```

How to solve this equation?