The histogram H of the gray image I or Y-component of YUV-image is the frequency of occurrence of each pixel level. For 8bpp the histogram is the vector of 256 elements (since pixel values are in the range 0..255).
It’s obvious that each image which is a spatial shuffling of pixels from the original image share same histogram.
For NxM image the number of permutations is (NxM)! but some pixels have same values therefore the exact number of images sharing the histogram H is:
Remind 0!=1
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