Generating a gaussian distributed cluster within a ring-shaped uniform distributed cluster in 2D

In Matlab, what would be the most elegant way to generate a cluster of Gaussian-distributed random points within a ring-shaped cluster of uniformly-distributed random points in 2D, where the following is given as input:

c - The clusters' center (share the same center)

sigma - the Gaussian-distributed cluster's radius (sigma = variance)

ng - the number of points in the Gaussian-distributed cluster

r - the radius of the ring-shaped cluster

w - the width of the ring

nr - the number of points in the ring-shaped, uniformly-distributed cluster

Thanks